Class C7a: Gamma, log gamma, reciprocal gamma functions
General Information
- Parent Class
- C7
- Top of Tree
- GAMS
- Keywords
- Complete gamma function, Digamma, Digamma function, Gamma, Gamma function, Gamma function, derivatives, Gamma, derivative of, Log gamma, Log gamma function, Mathematical Functions, Reciprocal gamma, Reciprocal gamma functions
Modules
Package AMOS (Downloadable)
- DGAMLN
- Ln gamma(x), for real x > 0.
- GAMLN
- Ln gamma(x), for real x > 0.
Package CEPHES (Downloadable)
- CPROB
- C routines for evaluation of probability distribution functions and their complements, inverses, and related functions. Among the distributions included are binomial, negative binomial, Beta, Chi-square, F, Gamma, normal, Poisson, and Student''s t. .
- QFLOAT
- C routines for extended-precision evaluation of mathematical functions. Includes makefiles, test programs, and a 100-digit calculator program.
Package CMLIB (Downloadable; Installed on ITL, ARNO)
- ALGAMS
- ln(abs(gamma(x))) and sign(gamma(x)).
- ALNGAM
- ln(abs(gamma(x))).
- CGAMMA
- gamma(z).
- CGAMR
- 1/gamma(z).
- CLNGAM
- ln(gamma(z)).
- DGAMMA
- gamma(x), for double precision x.
- DGAMR
- 1/gamma(x), for double precision x.
- DLGAMS
- ln(abs(gamma(x))) and sign(gamma(x)).
- DLNGAM
- ln(abs(gamma(x))).
- DPOCH
- Pochhammer''s symbol. Input and output are double precision.
- DPOCH1
- Pochhammer''s symbol from first order. Input and output are double precision.
- GAMLN
- ln(gamma(x)), for non-negative x.
- GAMMA
- gamma(x).
- GAMR
- 1/gamma(x).
- POCH
- Pochhammer''s symbol. Input and output are real.
- POCH1
- Pochhammer''s symbol from first order. Input and output are real.
Package FDLIBM (Downloadable)
- GAMMA
- Gamma(x). A portable C implementation for machines that support IEEE 754 floating point arithmetic. A wrapper routine is provided for other standards such as SVID, X/OPEN, or POSIX/ANSI.
- LGAMMA
- Log(gamma(x)). A portable C implementation for machines that support IEEE 754 floating point arithmetic. A wrapper routine is provided for other standards such as SVID, X/OPEN, or POSIX/ANSI.
Package FN (Downloadable)
- ALGAMS
- Ln(abs(gamma(x))) and sign(gamma(x)).
- ALNGAM
- Ln(abs(gamma(x))).
- CGAMMA
- Gamma(z).
- CGAMR
- 1/gamma(z).
- CLNGAM
- Ln(gamma(z)).
- DGAMMA
- Gamma(x).
- DGAMR
- 1/gamma(x).
- DLGAMS
- Ln(abs(gamma(x))) and sign(gamma(x)).
- DLNGAM
- Ln(abs(gamma(x))).
- DPOCH
- Pochhammer''s symbol.
- DPOCH1
- Pochhammer''s symbol from first order.
- GAMMA
- Gamma(x).
- GAMR
- 1/gamma(x).
- POCH
- Pochhammer''s symbol. Input and output are real.
- POCH1
- Pochhammer''s symbol from first order. Input and output are real.
Package IMSLM (Installed on ITL)
- ALGAMS
- Ln(abs(gamma(x))) and sign(gamma(x)).
- ALNGAM
- Ln(abs(gamma(x))).
- CGAMMA
- Complex gamma function.
- CGAMR
- 1/gamma(z).
- CLNGAM
- Ln(gamma(z)).
- CPSI
- Logarithmic derivative of the gamma function for a complex argument.
- DGAMMA
- gamma(x), for double precision x.
- DGAMR
- 1/gamma(x), for double precision x.
- DLGAMS
- Return the logarithm of the absolute value of the gamma function and the sign of gamma.
- DLNGAM
- Ln(abs(gamma(x))).
- DPOCH
- Pochhammer''s symbol. Input and output are double precision.
- DPOCH1
- Pochhammer''s symbol from first order. Input and output are double precision.
- GAMMA
- gamma(x).
- GAMR
- 1/gamma(x).
- POCH
- Generalization of Pochhammer''s symbol.
- POCH1
- Generalization of Pochhammer''s symbol starting from first order.
Package IMSLS (Installed on ITL)
- DGAMMA
- gamma(x), for double precision x.
- GAMMA
- gamma(x).
- s14aac
- Gamma function Γ(x)
- s14abc
- Log gamma function ln(Γ(x))
Package NMS (Installed on ITL)
- DGAMMA
- gamma(x), for double precision x.
- GAMMA
- gamma(x).
Package SLATEC (Downloadable; Installed on ITL, ARNO)
- ALGAMS
- Compute the logarithm of the absolute value of the Gamma function.
- ALNGAM
- Compute the logarithm of the absolute value of the Gamma function.
- C0LGMC
- Evaluate (Z+0.5)*LOG((Z+1.)/Z) 1.0 with relative accuracy.
- CGAMMA
- Compute the complete Gamma function.
- CGAMR
- Compute the reciprocal of the Gamma function.
- CLNGAM
- Compute the logarithm of the absolute value of the Gamma function.
- DGAMLM
- Compute the minimum and maximum bounds for the argument in the Gamma function.
- DGAMMA
- Compute the complete Gamma function.
- DGAMR
- Compute the reciprocal of the Gamma function.
- DLGAMS
- Compute the logarithm of the absolute value of the Gamma function.
- DLNGAM
- Compute the logarithm of the absolute value of the Gamma function.
- DPOCH
- Evaluate a generalization of Pochhammer''s symbol.
- DPOCH1
- Calculate a generalization of Pochhammer''s symbol starting from first order.
- GAMLIM
- Compute the minimum and maximum bounds for the argument in the Gamma function.
- GAMMA
- Compute the complete Gamma function.
- GAMR
- Compute the reciprocal of the Gamma function.
- POCH
- Evaluate a generalization of Pochhammer''s symbol.
- POCH1
- Calculate a generalization of Pochhammer''s symbol starting from first order.
Package SPECFUN (Downloadable)
- ALGAMA
- Calculates the LOG(GAMMA) function for a positive real argument X. Uses rationa functions that theoretically approximate LOG(GAMMA) to at least 18 significant decimal digits.
- GAMMA
- Calculates the GAMMA function for a real argument X. Uses rational functions that approximate the GAMMA function to at least 20 significant decimal digits.
Package TOMS (Downloadable)
- 814
- FM: Multiple precision arithmetic, and evalution of gamma and related functions, such as psi (digamma), polygamma, beta, incomplete gamma, incomplete beta, Bernoulli numbers, and Pochhammer''s symbol. (See D. Smith, ACM TOMS 27 (2001) pp. 377-387).