gamrn.f
REAL FUNCTION GAMRN (X)
C***BEGIN PROLOGUE GAMRN
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Warning: this routine is not intended to be user-callable.
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C***SUBSIDIARY
C***PURPOSE Subsidiary to BSKIN
C***LIBRARY SLATEC
C***TYPE SINGLE PRECISION (GAMRN-S, DGAMRN-D)
C***AUTHOR Amos, D. E., (SNLA)
C***DESCRIPTION
C
C Abstract
C GAMRN computes the GAMMA function ratio GAMMA(X)/GAMMA(X+0.5)
C for real X.gt.0. If X.ge.XMIN, an asymptotic expansion is
C evaluated. If X.lt.XMIN, an integer is added to X to form a
C new value of X.ge.XMIN and the asymptotic expansion is eval-
C uated for this new value of X. Successive application of the
C recurrence relation
C
C W(X)=W(X+1)*(1+0.5/X)
C
C reduces the argument to its original value. XMIN and comp-
C utational tolerances are computed as a function of the number
C of digits carried in a word by calls to I1MACH and R1MACH.
C However, the computational accuracy is limited to the max-
C imum of unit roundoff (=R1MACH(4)) and 1.0E-18 since critical
C constants are given to only 18 digits.
C
C Input
C X - Argument, X.gt.0.0
C
C OUTPUT
C GAMRN - Ratio GAMMA(X)/GAMMA(X+0.5)
C
C***SEE ALSO BSKIN
C***REFERENCES Y. L. Luke, The Special Functions and Their
C Approximations, Vol. 1, Math In Sci. And
C Eng. Series 53, Academic Press, New York, 1969,
C pp. 34-35.
C***ROUTINES CALLED I1MACH, R1MACH
C***REVISION HISTORY (YYMMDD)
C 820601 DATE WRITTEN
C 890531 Changed all specific intrinsics to generic. (WRB)
C 891214 Prologue converted to Version 4.0 format. (BAB)
C 900328 Added TYPE section. (WRB)
C 910722 Updated AUTHOR section. (ALS)
C 920520 Added REFERENCES section. (WRB)
C***END PROLOGUE GAMRN