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/Γ(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 Γ(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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