# dgamit.f

          DOUBLE PRECISION FUNCTION DGAMIT (A, X)
    C***BEGIN PROLOGUE  DGAMIT
    C***PURPOSE  Calculate Tricomi's form of the incomplete Gamma function.
    C***LIBRARY   SLATEC (FNLIB)
    C***CATEGORY  C7E
    C***TYPE      DOUBLE PRECISION (GAMIT-S, DGAMIT-D)
    C***KEYWORDS  COMPLEMENTARY INCOMPLETE GAMMA FUNCTION, FNLIB,
    C             SPECIAL FUNCTIONS, TRICOMI
    C***AUTHOR  Fullerton, W., (LANL)
    C***DESCRIPTION
    C
    C   Evaluate Tricomi's incomplete Gamma function defined by
    C
    C   DGAMIT = X**(-A)/GAMMA(A) * integral from 0 to X of EXP(-T) *
    C              T**(A-1.)
    C
    C   for A .GT. 0.0 and by analytic continuation for A .LE. 0.0.
    C   GAMMA(X) is the complete gamma function of X.
    C
    C   DGAMIT is evaluated for arbitrary real values of A and for non-
    C   negative values of X (even though DGAMIT is defined for X .LT.
    C   0.0), except that for X = 0 and A .LE. 0.0, DGAMIT is infinite,
    C   which is a fatal error.
    C
    C   The function and both arguments are DOUBLE PRECISION.
    C
    C   A slight deterioration of 2 or 3 digits accuracy will occur when
    C   DGAMIT is very large or very small in absolute value, because log-
    C   arithmic variables are used.  Also, if the parameter  A  is very
    C   close to a negative integer (but not a negative integer), there is
    C   a loss of accuracy, which is reported if the result is less than
    C   half machine precision.
    C
    C***REFERENCES  W. Gautschi, A computational procedure for incomplete
    C                 gamma functions, ACM Transactions on Mathematical
    C                 Software 5, 4 (December 1979), pp. 466-481.
    C               W. Gautschi, Incomplete gamma functions, Algorithm 542,
    C                 ACM Transactions on Mathematical Software 5, 4
    C                 (December 1979), pp. 482-489.
    C***ROUTINES CALLED  D1MACH, D9GMIT, D9LGIC, D9LGIT, DGAMR, DLGAMS,
    C                    DLNGAM, XERCLR, XERMSG
    C***REVISION HISTORY  (YYMMDD)
    C   770701  DATE WRITTEN
    C   890531  Changed all specific intrinsics to generic.  (WRB)
    C   890531  REVISION DATE from Version 3.2
    C   891214  Prologue converted to Version 4.0 format.  (BAB)
    C   900315  CALLs to XERROR changed to CALLs to XERMSG.  (THJ)
    C   920528  DESCRIPTION and REFERENCES sections revised.  (WRB)
    C***END PROLOGUE  DGAMIT