ALNGAM

The function evaluates the logarithm of the absolute value of the gamma function.

Required Arguments

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

FORTRAN 90 Interface

Generic: ALNGAM (X)

Specific: The specific interface names are S_ALNGAM, D_ALNGAM, and C_ALNGAM.

FORTRAN 77 Interface

Single: ALNGAM (X)

Double: The double precision function name is DLNGAM.

Complex: The complex name is CLNGAM.

Description

The function ALNGAM computes ln ∣Γ(x)∣. See GAMMA for the definition of Γ(x).

The gamma function is not defined for integers less than or equal to zero. Also, ∣x∣ must not be so large that the result overflows. Neither should x be so close to a negative integer that the accuracy is worse than half precision.

Figure 1, Plot of log∣Γ(x)∣

Comments

Informational Error

Type	Code	Description
3	2	Result of ALNGAM(X) is accurate to less than one‑half precision because X is too near a negative integer.

Examples

Example 1

In this example, ln ∣Γ(1.85)∣ is computed and printed.

USE ALNGAM_INT

USE UMACH_INT

IMPLICIT NONE

! Declare variables

INTEGER NOUT

REAL VALUE, X

! Compute

X = 1.85

VALUE = ALNGAM(X)

! Print the results

CALL UMACH (2, NOUT)

WRITE (NOUT,99999) X, VALUE

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

END

Output

ALNGAM( 1.850) = -0.056

Example 2

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

USE ALNGAM_INT

USE UMACH_INT

IMPLICIT NONE

! Declare variables

INTEGER NOUT

COMPLEX VALUE, Z

! Compute

Z = (1.4, 3.0)

VALUE = ALNGAM(Z)

! Print the results

CALL UMACH (2, NOUT)

WRITE (NOUT,99999) Z, VALUE

99999 FORMAT (' ALNGAM(', F6.3, ',', F6.3, ') = (',&

F6.3, ',', F6.3, ')')

END

Output

ALNGAM( 1.400, 3.000) = (-2.795, 1.589)