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B

Beta - Class in org.apache.commons.numbers.gamma

Beta function.

C

complement(double, double, double) - Static method in class org.apache.commons.numbers.gamma.IncompleteBeta

Computes the complement of the incomplete beta function B(x, a, b).

complement(double, double, double) - Static method in class org.apache.commons.numbers.gamma.RegularizedBeta

Computes the complement of the regularized beta function I(x, a, b).

complement(double, double, double, double, int) - Static method in class org.apache.commons.numbers.gamma.IncompleteBeta

Computes the complement of the incomplete beta function B(x, a, b).

complement(double, double, double, double, int) - Static method in class org.apache.commons.numbers.gamma.RegularizedBeta

Computes the complement of the regularized beta function I(x, a, b).

D

delta(double, double) - Static method in class org.apache.commons.numbers.gamma.GammaRatio

Computes the ratio of gamma functions of a value and an offset value.

derivative(double, double) - Static method in class org.apache.commons.numbers.gamma.RegularizedGamma.P

Computes the derivative of the lower regularized gamma function \( P(a, x) \).

derivative(double, double) - Static method in class org.apache.commons.numbers.gamma.RegularizedGamma.Q

Computes the derivative of the upper regularized gamma function \( Q(a, x) \).

derivative(double, double, double) - Static method in class org.apache.commons.numbers.gamma.RegularizedBeta

Computes the derivative of the regularized beta function I(x, a, b).

Digamma - Class in org.apache.commons.numbers.gamma

Digamma function.

E

Erf - Class in org.apache.commons.numbers.gamma

Error function.

Erfc - Class in org.apache.commons.numbers.gamma

Complementary error function.

Erfcx - Class in org.apache.commons.numbers.gamma

Scaled complementary error function.

ErfDifference - Class in org.apache.commons.numbers.gamma

Computes the difference between error function values.

G

g() - Static method in class org.apache.commons.numbers.gamma.LanczosApproximation

Return the Lanczos constant \( g = \frac{607}{128} \).

Gamma - Class in org.apache.commons.numbers.gamma

Gamma function \( \Gamma(x) \).

GammaRatio - Class in org.apache.commons.numbers.gamma

Ratio of Gamma functions.

I

IncompleteBeta - Class in org.apache.commons.numbers.gamma

Incomplete Beta function.

IncompleteGamma - Class in org.apache.commons.numbers.gamma

Incomplete Gamma functions.

IncompleteGamma.Lower - Class in org.apache.commons.numbers.gamma

Lower incomplete Gamma function \( \gamma(a, x) \).

IncompleteGamma.Upper - Class in org.apache.commons.numbers.gamma

Upper incomplete Gamma function \( \Gamma(a, x) \).

InverseErf - Class in org.apache.commons.numbers.gamma

Inverse of the error function.

InverseErfc - Class in org.apache.commons.numbers.gamma

Inverse of the complementary error function.

L

LanczosApproximation - Class in org.apache.commons.numbers.gamma

Lanczos approximation to the Gamma function.

LogBeta - Class in org.apache.commons.numbers.gamma

Computes \( log_e B(p, q) \).

LogGamma - Class in org.apache.commons.numbers.gamma

Natural logarithm of the absolute value of \( \Gamma(x) \).

O

org.apache.commons.numbers.gamma - package org.apache.commons.numbers.gamma

Γ (Gamma) and Β (Beta) family of functions.

R

RegularizedBeta - Class in org.apache.commons.numbers.gamma

Regularized Beta function.

RegularizedGamma - Class in org.apache.commons.numbers.gamma

Regularized Gamma functions.

RegularizedGamma.P - Class in org.apache.commons.numbers.gamma

Lower regularized Gamma function \( P(a, x) \).

RegularizedGamma.Q - Class in org.apache.commons.numbers.gamma

Upper regularized Gamma function \( Q(a, x) \).

T

Trigamma - Class in org.apache.commons.numbers.gamma

Trigamma function.

V

value(double) - Static method in class org.apache.commons.numbers.gamma.Digamma

Computes the digamma function.

value(double) - Static method in class org.apache.commons.numbers.gamma.Erf

Returns the error function.

value(double) - Static method in class org.apache.commons.numbers.gamma.Erfc

Returns the complementary error function.

value(double) - Static method in class org.apache.commons.numbers.gamma.Erfcx

Returns the scaled complementary error function.

value(double) - Static method in class org.apache.commons.numbers.gamma.Gamma

Computes the value of \( \Gamma(x) \).

value(double) - Static method in class org.apache.commons.numbers.gamma.InverseErf

Returns the inverse error function.

value(double) - Static method in class org.apache.commons.numbers.gamma.InverseErfc

Returns the inverse complementary error function.

value(double) - Static method in class org.apache.commons.numbers.gamma.LanczosApproximation

Computes the Lanczos approximation.

value(double) - Static method in class org.apache.commons.numbers.gamma.LogGamma

Computes the function \( \ln \lvert \Gamma(x) \rvert \), the natural logarithm of the absolute value of \( \Gamma(x) \).

value(double) - Static method in class org.apache.commons.numbers.gamma.Trigamma

Computes the trigamma function.

value(double, double) - Static method in class org.apache.commons.numbers.gamma.Beta

Computes the value of the beta function B(a, b).

value(double, double) - Static method in class org.apache.commons.numbers.gamma.ErfDifference

The implementation uses either Erf or Erfc, depending on which provides the most precise result.

value(double, double) - Static method in class org.apache.commons.numbers.gamma.GammaRatio

Computes the ratio of gamma functions of two values.

value(double, double) - Static method in class org.apache.commons.numbers.gamma.IncompleteGamma.Lower

Computes the lower incomplete gamma function \( \gamma(a, x) \).

value(double, double) - Static method in class org.apache.commons.numbers.gamma.IncompleteGamma.Upper

Computes the upper incomplete gamma function \( \Gamma(a, x) \).

value(double, double) - Static method in class org.apache.commons.numbers.gamma.LogBeta

Returns the value of \( \log B(p, q) \) for \( 0 \leq x \leq 1 \) and \( p, q > 0 \).

value(double, double) - Static method in class org.apache.commons.numbers.gamma.RegularizedGamma.P

Computes the lower regularized gamma function \( P(a, x) \).

value(double, double) - Static method in class org.apache.commons.numbers.gamma.RegularizedGamma.Q

Computes the upper regularized gamma function \( Q(a, x) \).

value(double, double, double) - Static method in class org.apache.commons.numbers.gamma.IncompleteBeta

Computes the value of the incomplete beta function B(x, a, b).

value(double, double, double) - Static method in class org.apache.commons.numbers.gamma.RegularizedBeta

Computes the value of the regularized beta function I(x, a, b).

value(double, double, double, double, int) - Static method in class org.apache.commons.numbers.gamma.IncompleteBeta

Computes the value of the incomplete beta function B(x, a, b).

value(double, double, double, double, int) - Static method in class org.apache.commons.numbers.gamma.RegularizedBeta

Computes the value of the regularized beta function I(x, a, b).

value(double, double, double, int) - Static method in class org.apache.commons.numbers.gamma.IncompleteGamma.Lower

Computes the lower incomplete gamma function \( \gamma(a, x) \).

value(double, double, double, int) - Static method in class org.apache.commons.numbers.gamma.IncompleteGamma.Upper

Computes the upper incomplete gamma function \( \Gamma(a, x) \).

value(double, double, double, int) - Static method in class org.apache.commons.numbers.gamma.RegularizedGamma.P

Computes the lower regularized gamma function \( P(a, x) \).

value(double, double, double, int) - Static method in class org.apache.commons.numbers.gamma.RegularizedGamma.Q

Computes the upper regularized gamma function \( Q(a, x) \).

value(double, int[]) - Static method in class org.apache.commons.numbers.gamma.LogGamma

Computes the function \( \ln \lvert \Gamma(x) \rvert \), the natural logarithm of the absolute value of \( \Gamma(x) \).

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