Chapter 4: Gamma Function and Related Functions

Routines

Factorial Function

Evaluates the factorial, n!.......................................................................................... FAC

Evaluates the binomial coefficient........................................................................... BINOM

Gamma Function

Evaluates the real or complex gamma function, Γ(x).............................................. GAMMA

Evaluates the reciprocal of the real or complex gamma
function, 1/ Γ(x)..................................................................................................... GAMR

Evaluates the real or complex function, ln ǀγ|(x)ǀ................................................... ALNGAM

Evaluates the log abs gamma function and its sign............................................... ALGAMS

Incomplete Gamma Function

Evaluates the incomplete gamma function, γ(a,x)....................................................... GAMI

Evaluates the complementary incomplete gamma function,
Γ(a,x).................................................................................................................. GAMIC

Evaluates Tricomi's incomplete gamma function, γ*(a, x).......................................... GAMIT

Psi Function

Evaluates the real or complex psi function, ψ(x)............................................................ PSI

Evaluates the real psi1 function, ψ1(x)......................................................................... PSI1

Pochhammer's Function

Evaluates Pochhammer's generalized symbol, (a)x................................................... POCH

Evaluates Pochhammer's symbol starting
from the first order................................................................................................ POCH1

Beta Function

Evaluates the real or complex beta function, β(a,b).................................................... BETA

Evaluates the log of the real or complex beta function,
ln β(a,b)............................................................................................................. ALBETA

Evaluates the incomplete beta function, Ix(a,b)......................................................... BETAI



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