# psi.f

          FUNCTION PSI (X)
    C***BEGIN PROLOGUE  PSI
    C***PURPOSE  Compute the Psi (or Digamma) function.
    C***LIBRARY   SLATEC (FNLIB)
    C***CATEGORY  C7C
    C***TYPE      SINGLE PRECISION (PSI-S, DPSI-D, CPSI-C)
    C***KEYWORDS  DIGAMMA FUNCTION, FNLIB, PSI FUNCTION, SPECIAL FUNCTIONS
    C***AUTHOR  Fullerton, W., (LANL)
    C***DESCRIPTION
    C
    C PSI(X) calculates the psi (or digamma) function for real argument X.
    C PSI(X) is the logarithmic derivative of the gamma function of X.
    C
    C Series for PSI        on the interval  0.          to  1.00000D+00
    C                                        with weighted error   2.03E-17
    C                                         log weighted error  16.69
    C                               significant figures required  16.39
    C                                    decimal places required  17.37
    C
    C Series for APSI       on the interval  0.          to  2.50000D-01
    C                                        with weighted error   5.54E-17
    C                                         log weighted error  16.26
    C                               significant figures required  14.42
    C                                    decimal places required  16.86
    C
    C***REFERENCES  (NONE)
    C***ROUTINES CALLED  COT, CSEVL, INITS, R1MACH, XERMSG
    C***REVISION HISTORY  (YYMMDD)
    C   770401  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   920618  Removed space from variable names.  (RWC, WRB)
    C***END PROLOGUE  PSI