Package org.apache.commons.numbers.gamma

Γ (Gamma) and Β (Beta) family of functions. Implementation of InvGamma1pm1 and LogGamma1p is based on the algorithms described in

• Didonato and Morris (1986), Computation of the Incomplete Gamma Function Ratios and their Inverse, TOMS 12(4), 377-393,
• Didonato and Morris (1992), Algorithm 708: Significant Digit Computation of the Incomplete Beta Function Ratios, TOMS 18(3), 360-373,

and implemented in the NSWC Library of Mathematical Functions.

Class Summary

Class	Description
Beta	Beta function.
Digamma	Digamma function.
Erf	Error function.
Erfc	Complementary error function.
Erfcx	Scaled complementary error function.
ErfDifference	Computes the difference between error function values.
Gamma	Gamma function \( \Gamma(x) \).
GammaRatio	Ratio of Gamma functions.
IncompleteBeta	Incomplete Beta function.
IncompleteGamma	Incomplete Gamma functions.
IncompleteGamma.Lower	Lower incomplete Gamma function \( \gamma(a, x) \).
IncompleteGamma.Upper	Upper incomplete Gamma function \( \Gamma(a, x) \).
InverseErf	Inverse of the error function.
InverseErfc	Inverse of the complementary error function.
LanczosApproximation	Lanczos approximation to the Gamma function.
LogBeta	Computes \( log_e B(p, q) \).
LogGamma	Natural logarithm of the absolute value of \( \Gamma(x) \).
RegularizedBeta	Regularized Beta function.
RegularizedGamma	Regularized Gamma functions.
RegularizedGamma.P	Lower regularized Gamma function \( P(a, x) \).
RegularizedGamma.Q	Upper regularized Gamma function \( Q(a, x) \).
Trigamma	Trigamma function.