Package org.apfloat

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:

1.13.0

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.
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	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	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	exp(Apcomplex z)	Exponential function.
Apcomplex	expIntegralE(Apcomplex ν, Apcomplex z)	Exponential integral E.
Apcomplex	expIntegralEi(Apcomplex z)	Exponential integral Ei.
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.
Apfloat	glaisher()	The Glaisher-Kinkelin constant A.
Apfloat	glaisher(int radix)	The Glaisher-Kinkelin constant A.
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.
Apfloat	khinchin()	Khinchin's constant K.
Apfloat	khinchin(int radix)	Khinchin's constant K.
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	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	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	sinh(Apcomplex z)	Hyperbolic sine.
Apcomplex	sinhIntegral(Apcomplex z)	Hyperbolic sine integral.
Apcomplex	sinIntegral(Apcomplex z)	Sine integral.
Apcomplex	sqrt(Apcomplex z)	Square root.
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	zeta(Apcomplex s)	Riemann zeta function.
Apcomplex	zeta(Apcomplex s, Apcomplex a)	Hurwitz zeta function.

Methods inherited from class java.lang.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

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:

B_z(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:

E_ν(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:

J_ν(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:

I_ν(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:

Y_ν(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:

K_ν(z)

Throws:

ArithmeticException - If z is zero.

ApfloatRuntimeException

Since:

1.13.0

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

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.