# Class FixedPrecisionApcomplexHelper

java.lang.Object
org.apfloat.FixedPrecisionApcomplexHelper

Direct Known Subclasses:
  `FixedPrecisionApfloatHelper`

public class FixedPrecisionApcomplexHelper extends Object
Fixed-precision mathematical functions for complex numbers.

All results of the mathematical operations are set to have the specified precision. Also all input arguments are set to the specified precision before the operation. If the specified precision is not infinite, this helper class also avoids `InfiniteExpansionException` e.g. in case where it would happen with `ApcomplexMath.acos(Apcomplex.ZERO)`.

Since:
  1.5
Version:
  1.15.0
Author:
  Mikko Tommila

- ## Constructor Summary

  Constructors
  Constructor
  Description
  `FixedPrecisionApcomplexHelper(long precision)`
  Constructs an apcomplex fixed-precison helper with the specified precision.

- ## Method Summary

  Modifier and Type
  Method
  Description
  `Apfloat`
  `abs(Apcomplex z)`
  Absolute value.
  `Apcomplex`
  `acos(Apcomplex z)`
  Arc cosine.
  `Apcomplex`
  `acosh(Apcomplex z)`
  Hyperbolic arc cosine.
  `Apcomplex`
  `add(Apcomplex z, Apcomplex w)`
  Addition.
  `Apcomplex`
  `agm(Apcomplex a, Apcomplex b)`
  Arithmetic-geometric mean.
  `Apcomplex`
  `airyAi(Apcomplex z)`
  Airy function Ai.
  `Apcomplex`
  `airyAiPrime(Apcomplex z)`
  Derivative of the Airy function Ai.
  `Apcomplex`
  `airyBi(Apcomplex z)`
  Airy function Bi.
  `Apcomplex`
  `airyBiPrime(Apcomplex z)`
  Derivative of the Airy function Bi.
  `Apcomplex[]`
  `allRoots(Apcomplex z, int n)`
  All branches of a root.
  `Apcomplex`
  `angerJ(Apcomplex ν, Apcomplex z)`
  Anger function 𝐉.
  `Apfloat`
  `arg(Apcomplex z)`
  Complex angle.
  `Apcomplex`
  `asin(Apcomplex z)`
  Arc sine.
  `Apcomplex`
  `asinh(Apcomplex z)`
  Hyperbolic arc sine.
  `Apcomplex`
  `atan(Apcomplex z)`
  Arc tangent.
  `Apcomplex`
  `atanh(Apcomplex z)`
  Hyperbolic arc tangent.
  `Apfloat`
  `bernoulli(long n)`
  Bernoulli number.
  `Apfloat`
  `bernoulli(long n, int radix)`
  Bernoulli number.
  `Apcomplex`
  `bernoulliB(long n, Apcomplex z)`
  Bernoulli polynomial.
  `Apcomplex`
  `besselI(Apcomplex ν, Apcomplex z)`
  Modified Bessel function of the first kind.
  `Apcomplex`
  `besselJ(Apcomplex ν, Apcomplex z)`
  Bessel function of the first kind.
  `Apcomplex`
  `besselK(Apcomplex ν, Apcomplex z)`
  Modified Bessel function of the second kind.
  `Apcomplex`
  `besselY(Apcomplex ν, Apcomplex z)`
  Bessel function of the second kind.
  `Apcomplex`
  `beta(Apcomplex a, Apcomplex b)`
  Beta function.
  `Apcomplex`
  `beta(Apcomplex z, Apcomplex a, Apcomplex b)`
  Incomplete beta function.
  `Apcomplex`
  `beta(Apcomplex z1, Apcomplex z2, Apcomplex a, Apcomplex b)`
  Generalized incomplete beta function.
  `Apfloat`
  `binomial(long n, long k)`
  Binomial coefficient.
  `Apfloat`
  `binomial(long n, long k, int radix)`
  Binomial coefficient.
  `Apcomplex`
  `binomial(Apcomplex n, Apcomplex k)`
  Binomial coefficient.
  `Apfloat`
  `catalan()`
  Catalan's constant G.
  `Apfloat`
  `catalan(int radix)`
  Catalan's constant G.
  `Apcomplex`
  `cbrt(Apcomplex z)`
  Cube root.
  `Apcomplex`
  `chebyshevT(Apcomplex ν, Apcomplex z)`
  Chebyshev function of the first kind.
  `Apcomplex`
  `chebyshevU(Apcomplex ν, Apcomplex z)`
  Chebyshev function of the second kind.
  `Apcomplex`
  `conj(Apcomplex z)`
  Complex conjugate.
  `Apcomplex`
  `cos(Apcomplex z)`
  Cosine.
  `Apcomplex`
  `cosh(Apcomplex z)`
  Hyperbolic cosine.
  `Apcomplex`
  `coshIntegral(Apcomplex z)`
  Hyperbolic cosine integral.
  `Apcomplex`
  `cosIntegral(Apcomplex z)`
  Cosine integral.
  `Apcomplex`
  `digamma(Apcomplex z)`
  Digamma function.
  `Apcomplex`
  `divide(Apcomplex z, Apcomplex w)`
  Division.
  `Apfloat`
  `e()`
  e.
  `Apfloat`
  `e(int radix)`
  e.
  `Apcomplex`
  `ellipticE(Apcomplex z)`
  Complete elliptic integral of the second kind.
  `Apcomplex`
  `ellipticK(Apcomplex z)`
  Complete elliptic integral of the first kind.
  `Apcomplex`
  `erf(Apcomplex z)`
  Error function.
  `Apcomplex`
  `erfc(Apcomplex z)`
  Complementary error function.
  `Apcomplex`
  `erfi(Apcomplex z)`
  Imaginary error function.
  `Apfloat`
  `euler()`
  γ, the Euler-Mascheroni constant.
  `Apfloat`
  `euler(int radix)`
  γ, the Euler-Mascheroni constant.
  `Apcomplex`
  `eulerE(long n, Apcomplex z)`
  Euler polynomial.
  `Apcomplex`
  `exp(Apcomplex z)`
  Exponential function.
  `Apcomplex`
  `expIntegralE(Apcomplex ν, Apcomplex z)`
  Exponential integral E.
  `Apcomplex`
  `expIntegralEi(Apcomplex z)`
  Exponential integral Ei.
  `Apcomplex`
  `fibonacci(Apcomplex ν, Apcomplex z)`
  Fibonacci function.
  `Apcomplex`
  `fresnelC(Apcomplex z)`
  Fresnel integral C.
  `Apcomplex`
  `fresnelS(Apcomplex z)`
  Fresnel integral S.
  `Apcomplex`
  `gamma(Apcomplex z)`
  Gamma function.
  `Apcomplex`
  `gamma(Apcomplex a, Apcomplex z)`
  Incomplete gamma function.
  `Apcomplex`
  `gamma(Apcomplex a, Apcomplex z0, Apcomplex z1)`
  Generalized incomplete gamma function.
  `Apcomplex`
  `gegenbauerC(Apcomplex ν, Apcomplex z)`
  Renormalized Gegenbauer function.
  `Apcomplex`
  `gegenbauerC(Apcomplex ν, Apcomplex λ, Apcomplex z)`
  Gegenbauer function.
  `Apfloat`
  `glaisher()`
  The Glaisher-Kinkelin constant A.
  `Apfloat`
  `glaisher(int radix)`
  The Glaisher-Kinkelin constant A.
  `Apcomplex`
  `harmonicNumber(Apcomplex z)`
  Harmonic number.
  `Apcomplex`
  `harmonicNumber(Apcomplex z, Apcomplex r)`
  Generalized harmonic number.
  `Apcomplex`
  `hermiteH(Apcomplex ν, Apcomplex z)`
  Hermite function.
  `Apcomplex`
  `hypergeometric0F1(Apcomplex a, Apcomplex z)`
  Confluent hypergeometric function 0F1.
  `Apcomplex`
  `hypergeometric0F1Regularized(Apcomplex a, Apcomplex z)`
  Regularized confluent hypergeometric function 0F̃1.
  `Apcomplex`
  `hypergeometric1F1(Apcomplex a, Apcomplex b, Apcomplex z)`
  Kummer confluent hypergeometric function 1F1.
  `Apcomplex`
  `hypergeometric1F1Regularized(Apcomplex a, Apcomplex b, Apcomplex z)`
  Regularized Kummer confluent hypergeometric function 1F̃1.
  `Apcomplex`
  `hypergeometric2F1(Apcomplex a, Apcomplex b, Apcomplex c, Apcomplex z)`
  Hypergeometric function 2F1.
  `Apcomplex`
  `hypergeometric2F1Regularized(Apcomplex a, Apcomplex b, Apcomplex c, Apcomplex z)`
  Regularized hypergeometric function 2F̃1.
  `Apcomplex`
  `hypergeometricU(Apcomplex a, Apcomplex b, Apcomplex z)`
  Tricomi's confluent hypergeometric function U.
  `Apfloat`
  `imag(Apcomplex z)`
  Imaginary part.
  `Apcomplex`
  `inverseRoot(Apcomplex z, long n)`
  Inverse root.
  `Apcomplex`
  `inverseRoot(Apcomplex z, long n, long k)`
  Inverse root with branch.
  `Apcomplex`
  `jacobiP(Apcomplex ν, Apcomplex a, Apcomplex b, Apcomplex z)`
  Jacobi function.
  `Apfloat`
  `khinchin()`
  Khinchin's constant K.
  `Apfloat`
  `khinchin(int radix)`
  Khinchin's constant K.
  `Apcomplex`
  `laguerreL(Apcomplex ν, Apcomplex z)`
  Laguerre function.
  `Apcomplex`
  `laguerreL(Apcomplex ν, Apcomplex λ, Apcomplex z)`
  Generalized Laguerre function.
  `Apcomplex`
  `legendreP(Apcomplex ν, Apcomplex z)`
  Legendre function.
  `Apcomplex`
  `legendreP(Apcomplex ν, Apcomplex μ, Apcomplex z)`
  Associated Legendre function of the first kind.
  `Apcomplex`
  `legendreQ(Apcomplex ν, Apcomplex z)`
  Legendre function of the second kind.
  `Apcomplex`
  `legendreQ(Apcomplex ν, Apcomplex μ, Apcomplex z)`
  Associated Legendre function of the second kind.
  `Apcomplex`
  `log(Apcomplex z)`
  Natural logarithm.
  `Apcomplex`
  `log(Apcomplex z, Apcomplex w)`
  Logarithm in specified base.
  `Apcomplex`
  `logGamma(Apcomplex z)`
  Logarithm of the gamma function.
  `Apcomplex`
  `logIntegral(Apcomplex z)`
  Logarithmic integral.
  `Apcomplex`
  `logisticSigmoid(Apcomplex z)`
  Logistic sigmoid.
  `Apcomplex`
  `multiply(Apcomplex z, Apcomplex w)`
  Multiplication.
  `Apcomplex`
  `negate(Apcomplex z)`
  Negation.
  `Apfloat`
  `norm(Apcomplex z)`
  Norm.
  `Apcomplex`
  `pochhammer(Apcomplex z, Apcomplex n)`
  Pochhammer symbol.
  `Apcomplex`
  `polygamma(long n, Apcomplex z)`
  Polygamma function.
  `Apcomplex`
  `polylog(Apcomplex ν, Apcomplex z)`
  Polylogarithm.
  `Apcomplex`
  `pow(Apcomplex z, long n)`
  Integer power.
  `Apcomplex`
  `pow(Apcomplex z, Apcomplex w)`
  Power.
  `long`
  `precision()`
  Returns the precision, which is used for the results.
  `Apcomplex`
  `product(Apcomplex... z)`
  Product.
  `Apfloat`
  `real(Apcomplex z)`
  Real part.
  `Apcomplex`
  `root(Apcomplex z, long n)`
  Root.
  `Apcomplex`
  `root(Apcomplex z, long n, long k)`
  Root with branch.
  `Apcomplex`
  `scale(Apcomplex z, long scale)`
  Move the radix point.
  `Apcomplex`
  `sin(Apcomplex z)`
  Sine.
  `Apcomplex`
  `sinc(Apcomplex z)`
  Sinc.
  `Apcomplex`
  `sinh(Apcomplex z)`
  Hyperbolic sine.
  `Apcomplex`
  `sinhIntegral(Apcomplex z)`
  Hyperbolic sine integral.
  `Apcomplex`
  `sinIntegral(Apcomplex z)`
  Sine integral.
  `Apcomplex`
  `sphericalHarmonicY(Apcomplex λ, Apcomplex μ, Apcomplex ϑ, Apcomplex ϕ)`
  Spherical harmonic function.
  `Apcomplex`
  `sqrt(Apcomplex z)`
  Square root.
  `Apcomplex`
  `struveH(Apcomplex ν, Apcomplex z)`
  Struve function 𝐇.
  `Apcomplex`
  `struveL(Apcomplex ν, Apcomplex z)`
  Modified Struve function 𝐋.
  `Apcomplex`
  `subtract(Apcomplex z, Apcomplex w)`
  Subtraction.
  `Apcomplex`
  `sum(Apcomplex... z)`
  Sum.
  `Apcomplex`
  `tan(Apcomplex z)`
  Tangent.
  `Apcomplex`
  `tanh(Apcomplex z)`
  Hyperbolic tangent.
  `Apfloat`
  `ulp(Apcomplex z)`
  Unit in the last place.
  `Apcomplex`
  `valueOf(Apcomplex z)`
  Returns the value with the specified precision.
  `Apcomplex`
  `w(Apcomplex z)`
  Lambert W function.
  `Apcomplex`
  `w(Apcomplex z, long k)`
  Lambert W function for the specified branch.
  `Apcomplex`
  `weberE(Apcomplex ν, Apcomplex z)`
  Weber function 𝐄.
  `Apcomplex`
  `zeta(Apcomplex s)`
  Riemann zeta function.
  `Apcomplex`
  `zeta(Apcomplex s, Apcomplex a)`
  Hurwitz zeta function.

  ### Methods inherited from class Object

  `clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

- ## Constructor Details

  - ### FixedPrecisionApcomplexHelper

    public FixedPrecisionApcomplexHelper(long precision) throws IllegalArgumentException
    Constructs an apcomplex fixed-precison helper with the specified precision. The results of all mathematical operations are set to the specified precision.
    Parameters:
      `precision` - The precision of the results.
    Throws:
      `IllegalArgumentException` - In case the precision is invalid.

- ## Method Details

  - ### valueOf

    public Apcomplex valueOf(Apcomplex z) throws ApfloatRuntimeException
    Returns the value with the specified precision.
    Parameters:
      `z` - The value.
    Returns:
      The value with to the specified precision.
    Throws:
      `ApfloatRuntimeException`

  - ### negate

    public Apcomplex negate(Apcomplex z) throws ApfloatRuntimeException
    Negation.
    Parameters:
      `z` - The value to negate.
    Returns:
      `-z`.
    Throws:
      `ApfloatRuntimeException`

  - ### conj

    public Apcomplex conj(Apcomplex z) throws ApfloatRuntimeException
    Complex conjugate.
    Parameters:
      `z` - The operand.
    Returns:
      `x - i y` where `z` is `x + i y`.
    Throws:
      `ApfloatRuntimeException`

  - ### add

    public Apcomplex add(Apcomplex z, Apcomplex w) throws ApfloatRuntimeException
    Addition.
    Parameters:
      `z` - The first operand.
      `w` - The second operand.
    Returns:
      `z + w`.
    Throws:
      `ApfloatRuntimeException`

  - ### subtract

    public Apcomplex subtract(Apcomplex z, Apcomplex w) throws ApfloatRuntimeException
    Subtraction.
    Parameters:
      `z` - The first operand.
      `w` - The second operand.
    Returns:
      `z - w`.
    Throws:
      `ApfloatRuntimeException`

  - ### multiply

    public Apcomplex multiply(Apcomplex z, Apcomplex w) throws ApfloatRuntimeException
    Multiplication.
    Parameters:
      `z` - The first operand.
      `w` - The second operand.
    Returns:
      `z * w`.
    Throws:
      `ApfloatRuntimeException`

  - ### divide

    public Apcomplex divide(Apcomplex z, Apcomplex w) throws ArithmeticException, ApfloatRuntimeException
    Division.
    Parameters:
      `z` - The first operand.
      `w` - The second operand.
    Returns:
      `z / w`.
    Throws:
      `ArithmeticException` - If `w` is zero.
      `ApfloatRuntimeException`

  - ### pow

    public Apcomplex pow(Apcomplex z, Apcomplex w) throws ArithmeticException, ApfloatRuntimeException
    Power.
    Parameters:
      `z` - The first operand.
      `w` - The second operand.
    Returns:
      `zw`.
    Throws:
      `ArithmeticException` - If `z` and `w` are zero.
      `ApfloatRuntimeException`

  - ### pow

    public Apcomplex pow(Apcomplex z, long n) throws ArithmeticException, ApfloatRuntimeException
    Integer power.
    Parameters:
      `z` - The first operand.
      `n` - The first operand.
    Returns:
      `zn`.
    Throws:
      `ArithmeticException` - If `z` and `n` are zero, or `z` is zero and `n` is negative.
      `ApfloatRuntimeException`

  - ### arg

    public Apfloat arg(Apcomplex z) throws ArithmeticException, ApfloatRuntimeException
    Complex angle.
    Parameters:
      `z` - The operand.
    Returns:
      The angle of `z` on the complex plane.
    Throws:
      `ArithmeticException` - If `z` is zero.
      `ApfloatRuntimeException`

  - ### imag

    public Apfloat imag(Apcomplex z)
    Imaginary part.
    Parameters:
      `z` - The operand.
    Returns:
      The imaginary part of `z`.

  - ### real

    public Apfloat real(Apcomplex z)
    Real part.
    Parameters:
      `z` - The operand.
    Returns:
      The real part of `z`.

  - ### abs

    public Apfloat abs(Apcomplex z) throws ApfloatRuntimeException
    Absolute value.
    Parameters:
      `z` - The operand.
    Returns:
      The absolute value of `z`.
    Throws:
      `ApfloatRuntimeException`

  - ### norm

    public Apfloat norm(Apcomplex z) throws ApfloatRuntimeException
    Norm.
    Parameters:
      `z` - The operand.
    Returns:
      `x2 + y2` where `z` is `x + i y`.
    Throws:
      `ApfloatRuntimeException`

  - ### acos

    public Apcomplex acos(Apcomplex z) throws ApfloatRuntimeException
    Arc cosine.
    Parameters:
      `z` - The operand.
    Returns:
      The arc cosine of `z`.
    Throws:
      `ApfloatRuntimeException`

  - ### acosh

    public Apcomplex acosh(Apcomplex z) throws ApfloatRuntimeException
    Hyperbolic arc cosine.
    Parameters:
      `z` - The operand.
    Returns:
      The hyperbolic arc cosine of `z`.
    Throws:
      `ApfloatRuntimeException`

  - ### asin

    public Apcomplex asin(Apcomplex z) throws ApfloatRuntimeException
    Arc sine.
    Parameters:
      `z` - The operand.
    Returns:
      The arc sine of `z`.
    Throws:
      `ApfloatRuntimeException`

  - ### asinh

    public Apcomplex asinh(Apcomplex z) throws ApfloatRuntimeException
    Hyperbolic arc sine.
    Parameters:
      `z` - The operand.
    Returns:
      The hyperbolic arc sine of `z`.
    Throws:
      `ApfloatRuntimeException`

  - ### atan

    public Apcomplex atan(Apcomplex z) throws ApfloatRuntimeException
    Arc tangent.
    Parameters:
      `z` - The operand.
    Returns:
      The arc tangent of `z`.
    Throws:
      `ArithmeticException` - If `z` is `i`.
      `ApfloatRuntimeException`

  - ### atanh

    public Apcomplex atanh(Apcomplex z) throws ArithmeticException, ApfloatRuntimeException
    Hyperbolic arc tangent.
    Parameters:
      `z` - The operand.
    Returns:
      The hyperbolic arc tangent of `z`.
    Throws:
      `ArithmeticException` - If `z` is 1 or -1.
      `ApfloatRuntimeException`

  - ### cbrt

    public Apcomplex cbrt(Apcomplex z) throws ApfloatRuntimeException
    Cube root.
    Parameters:
      `z` - The operand.
    Returns:
      The cube root of `z`.
    Throws:
      `ApfloatRuntimeException`

  - ### cos

    public Apcomplex cos(Apcomplex z) throws ApfloatRuntimeException
    Cosine.
    Parameters:
      `z` - The operand.
    Returns:
      The cosine of `z`.
    Throws:
      `ApfloatRuntimeException`

  - ### cosh

    public Apcomplex cosh(Apcomplex z) throws ApfloatRuntimeException
    Hyperbolic cosine.
    Parameters:
      `z` - The operand.
    Returns:
      The hyperbolic cosine of `z`.
    Throws:
      `ApfloatRuntimeException`

  - ### exp

    public Apcomplex exp(Apcomplex z) throws ApfloatRuntimeException
    Exponential function.
    Parameters:
      `z` - The operand.
    Returns:
      `ez`.
    Throws:
      `ApfloatRuntimeException`

  - ### log

    public Apcomplex log(Apcomplex z) throws ArithmeticException, ApfloatRuntimeException
    Natural logarithm.
    Parameters:
      `z` - The operand.
    Returns:
      The natural logarithm of `z`.
    Throws:
      `ArithmeticException` - If `z` is zero.
      `ApfloatRuntimeException`

  - ### log

    public Apcomplex log(Apcomplex z, Apcomplex w) throws ArithmeticException, ApfloatRuntimeException
    Logarithm in specified base.
    Parameters:
      `z` - The operand.
      `w` - The base.
    Returns:
      The base-`w` logarithm of `z`.
    Throws:
      `ArithmeticException` - If `z` or `w` is zero.
      `ApfloatRuntimeException`
    Since:
      1.6

  - ### sin

    public Apcomplex sin(Apcomplex z) throws ApfloatRuntimeException
    Sine.
    Parameters:
      `z` - The operand.
    Returns:
      The sine of `z`.
    Throws:
      `ApfloatRuntimeException`

  - ### sinh

    public Apcomplex sinh(Apcomplex z) throws ApfloatRuntimeException
    Hyperbolic sine.
    Parameters:
      `z` - The operand.
    Returns:
      The hyperbolic sine of `z`.
    Throws:
      `ApfloatRuntimeException`

  - ### sqrt

    public Apcomplex sqrt(Apcomplex z) throws ApfloatRuntimeException
    Square root.
    Parameters:
      `z` - The operand.
    Returns:
      The square root of `z`.
    Throws:
      `ApfloatRuntimeException`

  - ### tan

    public Apcomplex tan(Apcomplex z) throws ArithmeticException, ApfloatRuntimeException
    Tangent.
    Parameters:
      `z` - The operand.
    Returns:
      The tangent of `z`.
    Throws:
      `ArithmeticException` - If `z` is π/2 + n π where n is an integer.
      `ApfloatRuntimeException`

  - ### tanh

    public Apcomplex tanh(Apcomplex z) throws ArithmeticException, ApfloatRuntimeException
    Hyperbolic tangent.
    Parameters:
      `z` - The operand.
    Returns:
      The hyperbolic tangent of `z`.
    Throws:
      `ArithmeticException` - If `z` is i (π/2 + n π) where n is an integer.
      `ApfloatRuntimeException`

  - ### sinc

    public Apcomplex sinc(Apcomplex z) throws ApfloatRuntimeException
    Sinc.
    Parameters:
      `z` - The argument.
    Returns:
      sinc(z)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### agm

    public Apcomplex agm(Apcomplex a, Apcomplex b) throws ApfloatRuntimeException
    Arithmetic-geometric mean.
    Parameters:
      `a` - The first operand.
      `b` - The first operand.
    Returns:
      The arithmetic-geometric mean of `a` and `b`.
    Throws:
      `ApfloatRuntimeException`

  - ### inverseRoot

    public Apcomplex inverseRoot(Apcomplex z, long n) throws ArithmeticException, ApfloatRuntimeException
    Inverse root.
    Parameters:
      `z` - The operand.
      `n` - Which inverse root to take.
    Returns:
      `z-1/n`.
    Throws:
      `ArithmeticException` - If `z` or `n` is zero.
      `ApfloatRuntimeException`

  - ### inverseRoot

    public Apcomplex inverseRoot(Apcomplex z, long n, long k) throws ArithmeticException, ApfloatRuntimeException
    Inverse root with branch.
    Parameters:
      `z` - The operand.
      `n` - Which inverse root to take.
      `k` - Which branch to take.
    Returns:
      `z-1/ne-i2πk/n`.
    Throws:
      `ArithmeticException` - If `z` or `n` is zero.
      `ApfloatRuntimeException`

  - ### root

    public Apcomplex root(Apcomplex z, long n) throws ArithmeticException, ApfloatRuntimeException
    Root.
    Parameters:
      `z` - The operand.
      `n` - Which root to take.
    Returns:
      `z1/n`.
    Throws:
      `ArithmeticException` - If `n` is zero, or `z` is zero and `n` is negative.
      `ApfloatRuntimeException`

  - ### root

    public Apcomplex root(Apcomplex z, long n, long k) throws ArithmeticException, ApfloatRuntimeException
    Root with branch.
    Parameters:
      `z` - The operand.
      `n` - Which root to take.
      `k` - Which branch to take.
    Returns:
      `z1/nei2πsk/n` where `s` is the signum of the imaginary part of `z`.
    Throws:
      `ArithmeticException` - If `n` is zero, or `z` is zero and `n` is negative.
      `ApfloatRuntimeException`

  - ### allRoots

    public Apcomplex[] allRoots(Apcomplex z, int n) throws ArithmeticException, ApfloatRuntimeException
    All branches of a root.
    Parameters:
      `z` - The operand.
      `n` - Which root to take.
    Returns:
      `z1/n`.
    Throws:
      `ArithmeticException` - If `n` is zero, or `z` is zero and `n` is negative.
      `ApfloatRuntimeException`

  - ### scale

    public Apcomplex scale(Apcomplex z, long scale) throws ApfloatRuntimeException
    Move the radix point.
    Parameters:
      `z` - The operand.
      `scale` - The amount to move the radix point.
    Returns:
      `z * z.radix()scale`.
    Throws:
      `ApfloatRuntimeException`

  - ### w

    public Apcomplex w(Apcomplex z) throws ApfloatRuntimeException
    Lambert W function.
    Parameters:
      `z` - The operand.
    Returns:
      `W0(z)`.
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.8.0

  - ### w

    public Apcomplex w(Apcomplex z, long k) throws ApfloatRuntimeException
    Lambert W function for the specified branch.
    Parameters:
      `z` - The operand.
      `k` - The branch.
    Returns:
      `Wk(z)`.
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.8.0

  - ### product

    public Apcomplex product(Apcomplex... z) throws ApfloatRuntimeException
    Product.
    Parameters:
      `z` - The operand(s).
    Returns:
      The product of the operands.
    Throws:
      `ApfloatRuntimeException`

  - ### sum

    public Apcomplex sum(Apcomplex... z) throws ApfloatRuntimeException
    Sum.
    Parameters:
      `z` - The operand(s).
    Returns:
      The sum of the operands.
    Throws:
      `ApfloatRuntimeException`

  - ### e

    public Apfloat e() throws ApfloatRuntimeException
    e.
    Returns:
      e.
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.11.0

  - ### e

    public Apfloat e(int radix) throws NumberFormatException, ApfloatRuntimeException
    e.
    Parameters:
      `radix` - The radix of the result.
    Returns:
      e.
    Throws:
      `NumberFormatException` - If the radix is invalid.
      `ApfloatRuntimeException`
    Since:
      1.11.0

  - ### euler

    public Apfloat euler() throws ApfloatRuntimeException
    γ, the Euler-Mascheroni constant.
    Returns:
      `γ`.
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.11.0

  - ### euler

    public Apfloat euler(int radix) throws NumberFormatException, ApfloatRuntimeException
    γ, the Euler-Mascheroni constant.
    Parameters:
      `radix` - The radix of the result.
    Returns:
      `γ`.
    Throws:
      `NumberFormatException` - If the radix is invalid.
      `ApfloatRuntimeException`
    Since:
      1.11.0

  - ### catalan

    public Apfloat catalan() throws ApfloatRuntimeException
    Catalan's constant G.
    Returns:
      G.
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.11.0

  - ### catalan

    public Apfloat catalan(int radix) throws NumberFormatException, ApfloatRuntimeException
    Catalan's constant G.
    Parameters:
      `radix` - The radix of the result.
    Returns:
      G.
    Throws:
      `NumberFormatException` - If the radix is invalid.
      `ApfloatRuntimeException`
    Since:
      1.11.0

  - ### glaisher

    public Apfloat glaisher() throws ApfloatRuntimeException
    The Glaisher-Kinkelin constant A.
    Returns:
      A.
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.11.0

  - ### glaisher

    public Apfloat glaisher(int radix) throws NumberFormatException, ApfloatRuntimeException
    The Glaisher-Kinkelin constant A.
    Parameters:
      `radix` - The radix of the result.
    Returns:
      A.
    Throws:
      `NumberFormatException` - If the radix is invalid.
      `ApfloatRuntimeException`
    Since:
      1.11.0

  - ### khinchin

    public Apfloat khinchin() throws ApfloatRuntimeException
    Khinchin's constant K.
    Returns:
      K.
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.11.0

  - ### khinchin

    public Apfloat khinchin(int radix) throws NumberFormatException, ApfloatRuntimeException
    Khinchin's constant K.
    Parameters:
      `radix` - The radix of the result.
    Returns:
      K.
    Throws:
      `NumberFormatException` - If the radix is invalid.
      `ApfloatRuntimeException`
    Since:
      1.11.0

  - ### gamma

    public Apcomplex gamma(Apcomplex z) throws ArithmeticException, ApfloatRuntimeException
    Gamma function.
    Parameters:
      `z` - The operand.
    Returns:
      `Γ(z)`.
    Throws:
      `ArithmeticException` - If `z` is a nonpositive integer.
      `ApfloatRuntimeException`
    Since:
      1.9.0

  - ### gamma

    public Apcomplex gamma(Apcomplex a, Apcomplex z) throws ArithmeticException, ApfloatRuntimeException
    Incomplete gamma function.
    Parameters:
      `a` - The first operand.
      `z` - The second operand.
    Returns:
      `Γ(a, z)`.
    Throws:
      `ArithmeticException` - If `a` is a nonpositive integer and `z` is zero.
      `ApfloatRuntimeException`
    Since:
      1.10.0

  - ### gamma

    public Apcomplex gamma(Apcomplex a, Apcomplex z0, Apcomplex z1) throws ArithmeticException, ApfloatRuntimeException
    Generalized incomplete gamma function.
    Parameters:
      `a` - The first operand.
      `z0` - The second operand.
      `z1` - The third operand.
    Returns:
      `Γ(a, z0)` - `Γ(a, z1)`.
    Throws:
      `ArithmeticException` - If `a` is a nonpositive integer and either `z0` or `z1` is zero.
      `ApfloatRuntimeException`
    Since:
      1.10.0

  - ### logGamma

    public Apcomplex logGamma(Apcomplex z) throws ArithmeticException, ApfloatRuntimeException
    Logarithm of the gamma function.
    Parameters:
      `z` - The argument.
    Returns:
      `logΓ(z)`
    Throws:
      `ArithmeticException` - If `z` is a nonpositive integer.
      `ApfloatRuntimeException`
    Since:
      1.11.0

  - ### digamma

    public Apcomplex digamma(Apcomplex z) throws ArithmeticException, ApfloatRuntimeException
    Digamma function.
    Parameters:
      `z` - The argument.
    Returns:
      `ψ(z)`
    Throws:
      `ArithmeticException` - If `z` is a nonpositive integer.
      `ApfloatRuntimeException`
    Since:
      1.11.0

  - ### polygamma

    public Apcomplex polygamma(long n, Apcomplex z) throws ArithmeticException, ApfloatRuntimeException
    Polygamma function.
    Parameters:
      `n` - The order.
      `z` - The argument.
    Returns:
      `ψ(n)(z)`
    Throws:
      `ArithmeticException` - If `n` is negative or `z` is a nonpositive integer.
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### beta

    public Apcomplex beta(Apcomplex a, Apcomplex b) throws ArithmeticException, ApfloatRuntimeException
    Beta function.
    Parameters:
      `a` - The first argument.
      `b` - The second argument.
    Returns:
      B(a, b)
    Throws:
      `ArithmeticException` - If `a` or `b` is a nonpositive integer but `a + b` is not. Also if both `a` and `b` are nonpositive integers.
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### beta

    public Apcomplex beta(Apcomplex z, Apcomplex a, Apcomplex b) throws ArithmeticException, ApfloatRuntimeException
    Incomplete beta function.
    Parameters:
      `z` - The first argument.
      `a` - The second argument.
      `b` - The third argument.
    Returns:
      Bz(a, b)
    Throws:
      `ArithmeticException` - If `a` is a nonpositive integer or `z` is zero and `a` has nonpositive real part.
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### beta

    public Apcomplex beta(Apcomplex z1, Apcomplex z2, Apcomplex a, Apcomplex b) throws ArithmeticException, ApfloatRuntimeException
    Generalized incomplete beta function.
    Parameters:
      `z1` - The first argument.
      `z2` - The second argument.
      `a` - The third argument.
      `b` - The fourth argument.
    Returns:
      B(z1, z2)(a, b)
    Throws:
      `ArithmeticException` - If `a` is a nonpositive integer or `z1` or `z2` is zero and `a` has nonpositive real part.
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### pochhammer

    public Apcomplex pochhammer(Apcomplex z, Apcomplex n) throws ArithmeticException, ApfloatRuntimeException
    Pochhammer symbol.
    Parameters:
      `z` - The first argument.
      `n` - The second argument.
    Returns:
      `(z)n`
    Throws:
      `ArithmeticException` - If `z + n` is a nonpositive integer but `z` is not.
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### binomial

    public Apfloat binomial(long n, long k) throws ArithmeticException, ApfloatRuntimeException
    Binomial coefficient.
    Parameters:
      `n` - The argument.
      `k` - The argument.
    Returns:
      The binomial coefficient.
    Throws:
      `ArithmeticException` - If `n` or `k` is negative.
      `ApfloatRuntimeException`
    Since:
      1.11.0

  - ### binomial

    public Apfloat binomial(long n, long k, int radix) throws ArithmeticException, NumberFormatException, ApfloatRuntimeException
    Binomial coefficient.
    Parameters:
      `n` - The argument.
      `k` - The argument.
      `radix` - The radix.
    Returns:
      The binomial coefficient.
    Throws:
      `ArithmeticException` - If `n` or `k` is negative.
      `NumberFormatException` - If the radix is not valid.
      `ApfloatRuntimeException`
    Since:
      1.11.0

  - ### binomial

    public Apcomplex binomial(Apcomplex n, Apcomplex k) throws ArithmeticException, ApfloatRuntimeException
    Binomial coefficient.
    Parameters:
      `n` - The argument.
      `k` - The argument.
    Returns:
      The binomial coefficient.
    Throws:
      `ArithmeticException` - If `n`, `k` or `n - k` is a nonpositive integer.
      `ApfloatRuntimeException`
    Since:
      1.11.0

  - ### bernoulli

    public Apfloat bernoulli(long n) throws IllegalArgumentException, ApfloatRuntimeException
    Bernoulli number.
    Parameters:
      `n` - The argument.
    Returns:
      `Bn`
    Throws:
      `IllegalArgumentException` - If `n < 0`.
      `ApfloatRuntimeException`
    Since:
      1.11.0

  - ### bernoulli

    public Apfloat bernoulli(long n, int radix) throws IllegalArgumentException, NumberFormatException, ApfloatRuntimeException
    Bernoulli number.
    Parameters:
      `n` - The argument.
      `radix` - The radix.
    Returns:
      `Bn`
    Throws:
      `IllegalArgumentException` - If `n < 0`.
      `NumberFormatException` - If the radix is not valid.
      `ApfloatRuntimeException`
    Since:
      1.11.0

  - ### zeta

    public Apcomplex zeta(Apcomplex s) throws ArithmeticException, ApfloatRuntimeException
    Riemann zeta function.
    Parameters:
      `s` - The argument.
    Returns:
      `ζ(s)`
    Throws:
      `ArithmeticException` - If `s` is `1`.
      `ApfloatRuntimeException`
    Since:
      1.11.0

  - ### zeta

    public Apcomplex zeta(Apcomplex s, Apcomplex a) throws ArithmeticException, ApfloatRuntimeException
    Hurwitz zeta function.
    Parameters:
      `s` - The first argument.
      `a` - The second argument.
    Returns:
      `ζ(s, a)`
    Throws:
      `ArithmeticException` - If `s` is `1` or if `a` is a nonpositive integer.
      `ApfloatRuntimeException`
    Since:
      1.11.0

  - ### hypergeometric0F1

    public Apcomplex hypergeometric0F1(Apcomplex a, Apcomplex z) throws ArithmeticException, ApfloatRuntimeException
    Confluent hypergeometric function 0F1.
    Parameters:
      `a` - The first argument.
      `z` - The second argument.
    Returns:
      0F1(; a; z)
    Throws:
      `ArithmeticException` - If the function value is not finite.
      `ApfloatRuntimeException`
    Since:
      1.11.0

  - ### hypergeometric0F1Regularized

    public Apcomplex hypergeometric0F1Regularized(Apcomplex a, Apcomplex z) throws ApfloatRuntimeException
    Regularized confluent hypergeometric function 0F̃1.
    Parameters:
      `a` - The first argument.
      `z` - The second argument.
    Returns:
      0F̃1(; a; z)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### hypergeometric1F1

    public Apcomplex hypergeometric1F1(Apcomplex a, Apcomplex b, Apcomplex z) throws ArithmeticException, ApfloatRuntimeException
    Kummer confluent hypergeometric function 1F1.
    Parameters:
      `a` - The first argument.
      `b` - The second argument.
      `z` - The third argument.
    Returns:
      1F1(a; b; z)
    Throws:
      `ArithmeticException` - If the function value is not finite.
      `ApfloatRuntimeException`
    Since:
      1.11.0

  - ### hypergeometric1F1Regularized

    public Apcomplex hypergeometric1F1Regularized(Apcomplex a, Apcomplex b, Apcomplex z) throws ApfloatRuntimeException
    Regularized Kummer confluent hypergeometric function 1F̃1.
    Parameters:
      `a` - The first argument.
      `b` - The second argument.
      `z` - The third argument.
    Returns:
      1F̃1(a; b; z)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### hypergeometric2F1

    public Apcomplex hypergeometric2F1(Apcomplex a, Apcomplex b, Apcomplex c, Apcomplex z) throws ArithmeticException, ApfloatRuntimeException
    Hypergeometric function 2F1.
    Parameters:
      `a` - The first argument.
      `b` - The second argument.
      `c` - The third argument.
      `z` - The fourth argument.
    Returns:
      2F1(a, b; c; z)
    Throws:
      `ArithmeticException` - If the function value is not finite.
      `ApfloatRuntimeException`
    Since:
      1.11.0

  - ### hypergeometric2F1Regularized

    public Apcomplex hypergeometric2F1Regularized(Apcomplex a, Apcomplex b, Apcomplex c, Apcomplex z) throws ApfloatRuntimeException
    Regularized hypergeometric function 2F̃1.
    Parameters:
      `a` - The first argument.
      `b` - The second argument.
      `c` - The third argument.
      `z` - The fourth argument.
    Returns:
      2F̃1(a, b; c; z)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### hypergeometricU

    public Apcomplex hypergeometricU(Apcomplex a, Apcomplex b, Apcomplex z) throws ArithmeticException, ApfloatRuntimeException
    Tricomi's confluent hypergeometric function U.
    Parameters:
      `a` - The first argument.
      `b` - The second argument.
      `z` - The third argument.
    Returns:
      U(a, b, z)
    Throws:
      `ArithmeticException` - If the result is not finite.
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### erf

    public Apcomplex erf(Apcomplex z) throws ApfloatRuntimeException
    Error function.
    Parameters:
      `z` - The argument.
    Returns:
      erf(z)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### erfc

    public Apcomplex erfc(Apcomplex z) throws ApfloatRuntimeException
    Complementary error function.
    Parameters:
      `z` - The argument.
    Returns:
      erfc(z)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### erfi

    public Apcomplex erfi(Apcomplex z) throws ApfloatRuntimeException
    Imaginary error function.
    Parameters:
      `z` - The argument.
    Returns:
      erfi(z)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### fresnelS

    public Apcomplex fresnelS(Apcomplex z) throws ApfloatRuntimeException
    Fresnel integral S.
    Parameters:
      `z` - The argument.
    Returns:
      S(z)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### fresnelC

    public Apcomplex fresnelC(Apcomplex z) throws ApfloatRuntimeException
    Fresnel integral C.
    Parameters:
      `z` - The argument.
    Returns:
      C(z)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### expIntegralE

    public Apcomplex expIntegralE(Apcomplex ν, Apcomplex z) throws ArithmeticException, ApfloatRuntimeException
    Exponential integral E.
    Parameters:
      `ν` - The first argument.
      `z` - The second argument.
    Returns:
      Eν(z)
    Throws:
      `ArithmeticException` - If real part of `ν` is < 0 and `z` is zero.
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### expIntegralEi

    public Apcomplex expIntegralEi(Apcomplex z) throws ArithmeticException, ApfloatRuntimeException
    Exponential integral Ei.
    Parameters:
      `z` - The argument.
    Returns:
      Ei(z)
    Throws:
      `ArithmeticException` - If `z` is zero.
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### logIntegral

    public Apcomplex logIntegral(Apcomplex z) throws ArithmeticException, ApfloatRuntimeException
    Logarithmic integral.
    Parameters:
      `z` - The argument.
    Returns:
      li(z)
    Throws:
      `ArithmeticException` - If `z` is zero.
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### sinIntegral

    public Apcomplex sinIntegral(Apcomplex z) throws ApfloatRuntimeException
    Sine integral.
    Parameters:
      `z` - The argument.
    Returns:
      Si(z)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### cosIntegral

    public Apcomplex cosIntegral(Apcomplex z) throws ArithmeticException, ApfloatRuntimeException
    Cosine integral.
    Parameters:
      `z` - The argument.
    Returns:
      Ci(z)
    Throws:
      `ArithmeticException` - If `z` is zero.
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### sinhIntegral

    public Apcomplex sinhIntegral(Apcomplex z) throws ApfloatRuntimeException
    Hyperbolic sine integral.
    Parameters:
      `z` - The argument.
    Returns:
      Shi(z)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### coshIntegral

    public Apcomplex coshIntegral(Apcomplex z) throws ArithmeticException, ApfloatRuntimeException
    Hyperbolic cosine integral.
    Parameters:
      `z` - The argument.
    Returns:
      Chi(z)
    Throws:
      `ArithmeticException` - If `z` is zero.
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### airyAi

    public Apcomplex airyAi(Apcomplex z) throws ApfloatRuntimeException
    Airy function Ai.
    Parameters:
      `z` - The argument.
    Returns:
      Ai(z)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### airyAiPrime

    public Apcomplex airyAiPrime(Apcomplex z) throws ApfloatRuntimeException
    Derivative of the Airy function Ai.
    Parameters:
      `z` - The argument.
    Returns:
      Ai′(z)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### airyBi

    public Apcomplex airyBi(Apcomplex z) throws ApfloatRuntimeException
    Airy function Bi.
    Parameters:
      `z` - The argument.
    Returns:
      Bi(z)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### airyBiPrime

    public Apcomplex airyBiPrime(Apcomplex z) throws ApfloatRuntimeException
    Derivative of the Airy function Bi.
    Parameters:
      `z` - The argument.
    Returns:
      Bi′(z)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### besselJ

    public Apcomplex besselJ(Apcomplex ν, Apcomplex z) throws ArithmeticException, ApfloatRuntimeException
    Bessel function of the first kind.
    Parameters:
      `ν` - The order.
      `z` - The argument.
    Returns:
      Jν(z)
    Throws:
      `ArithmeticException` - If the real part of `ν` is < 0 and `ν` is not an integer and `z` is zero. Also if the real part of `ν` is zero but the imaginary part is not, and `z` is zero.
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### besselI

    public Apcomplex besselI(Apcomplex ν, Apcomplex z) throws ArithmeticException, ApfloatRuntimeException
    Modified Bessel function of the first kind.
    Parameters:
      `ν` - The order.
      `z` - The argument.
    Returns:
      Iν(z)
    Throws:
      `ArithmeticException` - If the real part of `ν` is < 0 and `ν` is not an integer and `z` is zero. Also if the real part of `ν` is zero but the imaginary part is not, and `z` is zero.
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### besselY

    public Apcomplex besselY(Apcomplex ν, Apcomplex z) throws ArithmeticException, ApfloatRuntimeException
    Bessel function of the second kind.
    Parameters:
      `ν` - The order.
      `z` - The argument.
    Returns:
      Yν(z)
    Throws:
      `ArithmeticException` - If `z` is zero.
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### besselK

    public Apcomplex besselK(Apcomplex ν, Apcomplex z) throws ArithmeticException, ApfloatRuntimeException
    Modified Bessel function of the second kind.
    Parameters:
      `ν` - The order.
      `z` - The argument.
    Returns:
      Kν(z)
    Throws:
      `ArithmeticException` - If `z` is zero.
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### struveH

    public Apcomplex struveH(Apcomplex ν, Apcomplex z) throws ArithmeticException, ApfloatRuntimeException
    Struve function 𝐇.

    Parameters:
      `ν` - The order.
      `z` - The argument.
    Returns:
      𝐇ν(z)
    Throws:
      `ArithmeticException` - If `z` is zero and real part of `ν` is ≤ -1.
      `ApfloatRuntimeException`
    Since:
      1.15.0

  - ### struveL

    public Apcomplex struveL(Apcomplex ν, Apcomplex z) throws ArithmeticException, ApfloatRuntimeException
    Modified Struve function 𝐋.

    Parameters:
      `ν` - The order.
      `z` - The argument.
    Returns:
      𝐋ν(z)
    Throws:
      `ArithmeticException` - If `z` is zero and real part of `ν` is ≤ -1.
      `ApfloatRuntimeException`
    Since:
      1.15.0

  - ### angerJ

    public Apcomplex angerJ(Apcomplex ν, Apcomplex z) throws ApfloatRuntimeException
    Anger function 𝐉.

    Parameters:
      `ν` - The order.
      `z` - The argument.
    Returns:
      𝐉ν(z)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.15.0

  - ### weberE

    public Apcomplex weberE(Apcomplex ν, Apcomplex z) throws ApfloatRuntimeException
    Weber function 𝐄.

    Parameters:
      `ν` - The order.
      `z` - The argument.
    Returns:
      𝐄ν(z)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.15.0

  - ### ellipticK

    public Apcomplex ellipticK(Apcomplex z) throws ArithmeticException, ApfloatRuntimeException
    Complete elliptic integral of the first kind.
    Parameters:
      `z` - The argument.
    Returns:
      K(z)
    Throws:
      `ArithmeticException` - If `z` is one.
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### ellipticE

    public Apcomplex ellipticE(Apcomplex z) throws ApfloatRuntimeException
    Complete elliptic integral of the second kind.
    Parameters:
      `z` - The argument.
    Returns:
      E(z)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### hermiteH

    public Apcomplex hermiteH(Apcomplex ν, Apcomplex z) throws ApfloatRuntimeException
    Hermite function.
    Parameters:
      `ν` - The first argument.
      `z` - The second argument.
    Returns:
      Hν(z)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### laguerreL

    public Apcomplex laguerreL(Apcomplex ν, Apcomplex z) throws ApfloatRuntimeException
    Laguerre function.
    Parameters:
      `ν` - The first argument.
      `z` - The second argument.
    Returns:
      Lν(z)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### laguerreL

    public Apcomplex laguerreL(Apcomplex ν, Apcomplex λ, Apcomplex z) throws ApfloatRuntimeException
    Generalized Laguerre function.
    Parameters:
      `ν` - The first argument.
      `λ` - The second argument.
      `z` - The third argument.
    Returns:
      Lνλ(z)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### legendreP

    public Apcomplex legendreP(Apcomplex ν, Apcomplex z) throws ArithmeticException, ApfloatRuntimeException
    Legendre function.
    Parameters:
      `ν` - The first argument.
      `z` - The second argument.
    Returns:
      Pν(z)
    Throws:
      `ArithmeticException` - If `ν` is not an integer and `z` is -1.
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### legendreP

    public Apcomplex legendreP(Apcomplex ν, Apcomplex μ, Apcomplex z) throws ArithmeticException, ApfloatRuntimeException
    Associated Legendre function of the first kind.
    Parameters:
      `ν` - The first argument.
      `μ` - The second argument.
      `z` - The third argument.
    Returns:
      Pνμ(z)
    Throws:
      `ArithmeticException` - If `ν` is not an integer and `z` is -1.
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### legendreQ

    public Apcomplex legendreQ(Apcomplex ν, Apcomplex z) throws ArithmeticException, ApfloatRuntimeException
    Legendre function of the second kind.
    Parameters:
      `ν` - The first argument.
      `z` - The second argument.
    Returns:
      Qν(z)
    Throws:
      `ArithmeticException` - If `z` is 1 or -1.
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### legendreQ

    public Apcomplex legendreQ(Apcomplex ν, Apcomplex μ, Apcomplex z) throws ArithmeticException, ApfloatRuntimeException
    Associated Legendre function of the second kind.
    Parameters:
      `ν` - The first argument.
      `μ` - The second argument.
      `z` - The third argument.
    Returns:
      Qνμ(z)
    Throws:
      `ArithmeticException` - If `z` is 1 or -1.
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### sphericalHarmonicY

    public Apcomplex sphericalHarmonicY(Apcomplex λ, Apcomplex μ, Apcomplex ϑ, Apcomplex ϕ) throws ArithmeticException, ApfloatRuntimeException
    Spherical harmonic function.
    Parameters:
      `λ` - The first argument.
      `μ` - The second argument.
      `ϑ` - The third argument.
      `ϕ` - The fourth argument.
    Returns:
      Yλμ(ϑ, φ)
    Throws:
      `ArithmeticException` - If `ϑ` is π plus a multiple of 2 π and μ is not an integer and has a negative real part, or if `λ - μ` is a negative integer.
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### chebyshevT

    public Apcomplex chebyshevT(Apcomplex ν, Apcomplex z) throws ApfloatRuntimeException
    Chebyshev function of the first kind.
    Parameters:
      `ν` - The first argument.
      `z` - The second argument.
    Returns:
      Tν(z)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### chebyshevU

    public Apcomplex chebyshevU(Apcomplex ν, Apcomplex z) throws ArithmeticException, ApfloatRuntimeException
    Chebyshev function of the second kind.
    Parameters:
      `ν` - The first argument.
      `z` - The second argument.
    Returns:
      Uν(z)
    Throws:
      `ArithmeticException` - If `z` is -1 and `ν` is not an integer.
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### gegenbauerC

    public Apcomplex gegenbauerC(Apcomplex ν, Apcomplex z) throws ArithmeticException, ApfloatRuntimeException
    Renormalized Gegenbauer function.
    Parameters:
      `ν` - The first argument.
      `z` - The second argument.
    Returns:
      Cν(0)(z)
    Throws:
      `ArithmeticException` - If `ν` is zero.
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### gegenbauerC

    public Apcomplex gegenbauerC(Apcomplex ν, Apcomplex λ, Apcomplex z) throws ArithmeticException, ApfloatRuntimeException
    Gegenbauer function.
    Parameters:
      `ν` - The first argument.
      `λ` - The second argument.
      `z` - The third argument.
    Returns:
      Cνλ(z)
    Throws:
      `ArithmeticException` - If `z` is -1 and real part of `λ` is > 1/2. Also if `z` is -1 and `λ` is 1/2 and `ν` is not an integer.
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### jacobiP

    public Apcomplex jacobiP(Apcomplex ν, Apcomplex a, Apcomplex b, Apcomplex z) throws ArithmeticException, ApfloatRuntimeException
    Jacobi function.
    Parameters:
      `ν` - The first argument.
      `a` - The second argument.
      `b` - The third argument.
      `z` - The fourth argument.
    Returns:
      Pν(a,b)(z)
    Throws:
      `ArithmeticException` - If `z` is -1 and real part of `b` is > 0 and `ν` is not a positive integer. Also if `ν + a` is a negative integer and `ν` is not an integer.
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### fibonacci

    public Apcomplex fibonacci(Apcomplex ν, Apcomplex z) throws ArithmeticException, ApfloatRuntimeException
    Fibonacci function.
    Parameters:
      `ν` - The first argument.
      `z` - The second argument.
    Returns:
      Fν(z)
    Throws:
      `ArithmeticException` - If `z` is -1 and `ν` is not an integer.
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### eulerE

    public Apcomplex eulerE(long n, Apcomplex z) throws IllegalArgumentException, ApfloatRuntimeException
    Euler polynomial.
    Parameters:
      `n` - The first argument.
      `z` - The second argument.
    Returns:
      En(z)
    Throws:
      `IllegalArgumentException` - If `n` < 0.
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### bernoulliB

    public Apcomplex bernoulliB(long n, Apcomplex z) throws IllegalArgumentException, ApfloatRuntimeException
    Bernoulli polynomial.
    Parameters:
      `n` - The first argument.
      `z` - The second argument.
    Returns:
      Bn(z)
    Throws:
      `IllegalArgumentException` - If `n` < 0.
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### harmonicNumber

    public Apcomplex harmonicNumber(Apcomplex z) throws ArithmeticException, ApfloatRuntimeException
    Harmonic number.
    Parameters:
      `z` - The argument.
    Returns:
      Hz
    Throws:
      `ArithmeticException` - If `z` is a negative integer.
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### harmonicNumber

    public Apcomplex harmonicNumber(Apcomplex z, Apcomplex r) throws ArithmeticException, ApfloatRuntimeException
    Generalized harmonic number.
    Parameters:
      `z` - The first argument.
      `r` - The second argument.
    Returns:
      Hz(r)
    Throws:
      `ArithmeticException` - If `z` is a negative integer, unless `r` has a negative real part or is zero.
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### polylog

    public Apcomplex polylog(Apcomplex ν, Apcomplex z) throws ArithmeticException, ApfloatRuntimeException
    Polylogarithm.
    Parameters:
      `ν` - The first argument.
      `z` - The second argument.
    Returns:
      Liν(z)
    Throws:
      `ArithmeticException` - If the real part of `ν` is ≤ 1 and `z` is 1.
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### logisticSigmoid

    public Apcomplex logisticSigmoid(Apcomplex z) throws ArithmeticException, ApfloatRuntimeException
    Logistic sigmoid.
    Parameters:
      `z` - The argument.
    Returns:
      σ(z)
    Throws:
      `ArithmeticException` - If `z` is an odd integer multiple of π i.
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### ulp

    public Apfloat ulp(Apcomplex z) throws ApfloatRuntimeException
    Unit in the last place.
    Parameters:
      `z` - The operand.
    Returns:
      The unit in the last place.
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.10.0

  - ### precision

    public long precision()
    Returns the precision, which is used for the results.
    Returns:
      The precision of the results.