C303 Gamma Function for Real Argument

Function subprograms GAMMF and DGAMMF calculate the gamma function

$\Gamma (x)\; =\; \int$₀^&inf;e^-tt^x-1dt(x > 0), Γ(x) = {πΓ(1-x) sinπx}(x<0)

for real argument $x\; \ne -n,(n\; =\; 0,1,2,...)$ .

On CDC and Cray computers, the double-precision version DGAMMF is not available.

Structure:

FUNCTION subprograms
User Entry Names: GAMMF, DGAMMF
Files Referenced: Unit 6
External References: MTLMTR (N002), ABEND (Z035)

Usage:

In any arithmetic expression, GAMMF(X) or DGAMMF(X) has the value $\Gamma (X)$ ,

where GAMMF is of type REAL, DGAMMF is of type DOUBLE PRECISION, and X has the same type as the function name.

Method:

Approximation by truncated Chebyshev series and functional relations.

Accuracy:

GAMMF (except on CDC and Cray computers) has full single-precision accuracy. DGAMMF (and of GAMMF on CDC and Cray computers) has an accuracy which is approximately one digit less than machine precision.

Error handling:

Error C303.1: $X=\; -n,(n\; =\; 0,1,2,...).$

The function value is set equal to zero, and a message is written on Unit 6, unless subroutine MTLSET (N002) has been called.

References:

1. Y.L. Luke, Mathematical functions and their approximations, (Academic Press, New York 1975) 4.

C304