SLATEC Routines --- POCH1 ---

*DECK POCH1
      FUNCTION POCH1 (A, X)
C***BEGIN PROLOGUE  POCH1
C***PURPOSE  Calculate a generalization of Pochhammer's symbol starting
C            from first order.
C***LIBRARY   SLATEC (FNLIB)
C***CATEGORY  C1, C7A
C***TYPE      SINGLE PRECISION (POCH1-S, DPOCH1-D)
C***KEYWORDS  FIRST ORDER, FNLIB, POCHHAMMER, SPECIAL FUNCTIONS
C***AUTHOR  Fullerton, W., (LANL)
C***DESCRIPTION
C
C Evaluate a generalization of Pochhammer's symbol for special
C situations that require especially accurate values when X is small in
C        POCH1(A,X) = (POCH(A,X)-1)/X
C                   = (GAMMA(A+X)/GAMMA(A) - 1.0)/X .
C This specification is particularly suited for stably computing
C expressions such as
C        (GAMMA(A+X)/GAMMA(A) - GAMMA(B+X)/GAMMA(B))/X
C             = POCH1(A,X) - POCH1(B,X)
C Note that POCH1(A,0.0) = PSI(A)
C
C When ABS(X) is so small that substantial cancellation will occur if
C the straightforward formula is used, we  use an expansion due
C to Fields and discussed by Y. L. Luke, The Special Functions and Their
C Approximations, Vol. 1, Academic Press, 1969, page 34.
C
C The ratio POCH(A,X) = GAMMA(A+X)/GAMMA(A) is written by Luke as
C        (A+(X-1)/2)**X * polynomial in (A+(X-1)/2)**(-2) .
C In order to maintain significance in POCH1, we write for positive A
C        (A+(X-1)/2)**X = EXP(X*LOG(A+(X-1)/2)) = EXP(Q)
C                       = 1.0 + Q*EXPREL(Q) .
C Likewise the polynomial is written
C        POLY = 1.0 + X*POLY1(A,X) .
C Thus,
C        POCH1(A,X) = (POCH(A,X) - 1) / X
C                   = EXPREL(Q)*(Q/X + Q*POLY1(A,X)) + POLY1(A,X)
C
C***REFERENCES  (NONE)
C***ROUTINES CALLED  COT, EXPREL, POCH, PSI, R1MACH, XERMSG
C***REVISION HISTORY  (YYMMDD)
C   770801  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   900727  Added EXTERNAL statement.  (WRB)
C***END PROLOGUE  POCH1