This function evaluates the reciprocal gamma function.

Function Return Value

GAMR —  Function value.   (Output)

Required Arguments

X — Argument for which the reciprocal gamma function is desired.   (Input)

FORTRAN 90 Interface

Generic:                              GAMR (X)

Specific:                             The specific interface names are S_GAMR, D_GAMR, and C_GAMR

FORTRAN 77 Interface

Single:                                GAMR (X)

Double:                              The double precision function name is DGAMR.

Complex:                            The complex name is CGAMR.

Description

The function GAMR computes 1/ Γ(z). See GAMMA for the definition of Γ(z).

For ℑ(z)≈ 0, z must be larger than xmin so that 1/ Γ(z) does not underflow, and x must be smaller than xmax so that 1/Γ(z) does not overflow. Symmetric overflow and underflow limits xmin and  xmax are obtainable from

CALL R9GAML (XMIN, XMAX)

Note that z must not be too far from the real axis because the result will overflow there.

Comments

This function is well behaved near zero and negative integers.

Example 1

In this example, 1/G(1.85) is computed and printed.

 

      USE GAMR_INT

      USE UMACH_INT

 

      IMPLICIT   NONE

!                                 Declare variables

      INTEGER    NOUT

      REAL       VALUE, X

!                                 Compute

      X     = 1.85

      VALUE = GAMR(X)

!                                 Print the results

      CALL UMACH (2, NOUT)

      WRITE (NOUT,99999) X, VALUE

99999 FORMAT (' GAMR(', F6.3, ') = ', F6.3)

      END

Output

 

GAMR( 1.850) =  1.058

Additional Example

Example 2

In this example, ln G(1.4 + 3i) is computed and printed.

 

      USE GAMR_INT

      USE UMACH_INT

 

      IMPLICIT   NONE

!                                 Declare variables

      INTEGER    NOUT

      COMPLEX    VALUE, Z

!                                 Compute

      Z     = (1.4, 3.0)

      VALUE = GAMR(Z)

!                                 Print the results

      CALL UMACH (2, NOUT)

      WRITE (NOUT,99999) Z, VALUE

99999 FORMAT (' GAMR(', F6.3, ',', F6.3, ') = (', F7.3, ',', F7.3, ')')

      END

Output

 

GAMR( 1.400, 3.000) = ( -0.303,-16.367)

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