DGAMIT(3)

SYNOPSIS
DOUBLE PRECISION FUNCTION DGAMIT (A, X)

NAME
dgamit - Calculate Tricomi's form of the incomplete Gamma function.

LIBRARY
SLATEC (FNLIB)

CATEGORY
C7E

TYPE
DOUBLE PRECISION (GAMIT-S, DGAMIT-D)

KEYWORDS
COMPLEMENTARY INCOMPLETE GAMMA FUNCTION, FNLIB, SPECIAL FUNCTIONS, TRICOMI

AUTHOR
Fullerton, W., (LANL)

DESCRIPTION
Evaluate Tricomi's incomplete Gamma function defined by DGAMIT = X**(-A)/GAMMA(A) * integral from 0 to X of EXP(-T) * T**(A-1.) for A .GT. 0.0 and by analytic continuation for A .LE. 0.0. GAMMA(X) is the complete gamma function of X. DGAMIT is evaluated for arbitrary real values of A and for non- negative values of X (even though DGAMIT is defined for X .LT. 0.0), except that for X = 0 and A .LE. 0.0, DGAMIT is infinite, which is a fatal error. The function and both arguments are DOUBLE PRECISION. A slight deterioration of 2 or 3 digits accuracy will occur when DGAMIT is very large or very small in absolute value, because log- arithmic variables are used. Also, if the parameter A is very close to a negative integer (but not a negative integer), there is a loss of accuracy, which is reported if the result is less than half machine precision.

REFERENCES
W. Gautschi, A computational procedure for incomplete gamma functions, ACM Transactions on Mathematical Software 5, 4 (December 1979), pp. 466-481. W. Gautschi, Incomplete gamma functions, Algorithm 542, ACM Transactions on Mathematical Software 5, 4 (December 1979), pp. 482-489.

ROUTINES CALLED
D1MACH, D9GMIT, D9LGIC, D9LGIT, DGAMR, DLGAMS, DLNGAM, XERCLR, XERMSG

REVISION HISTORY (YYMMDD)
770701 DATE WRITTEN
890531 Changed all specific intrinsics to generic. (WRB)
890531 REVISION DATE from Version 3.2
891214 Prologue converted to Version 4.0 format. (BAB)
900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ)
920528 DESCRIPTION and REFERENCES sections revised. (WRB)