PSI

This function evaluates the derivative of the log gamma function.

Required Arguments

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

FORTRAN 90 Interface

Generic: PSI (X)

Specific: The specific interface names are S_PSI, D_PSI, and C_PSI.

FORTRAN 77 Interface

Single: PSI (X)

Double: The double precision function name is DPSI.

Complex: The complex name is CPSI.

Description

The psi function, also called the digamma function, is defined to be

See GAMMA for the definition of Γ(x).

The argument x must not be exactly zero or a negative integer, or ψ (x) is undefined. Also, x must not be too close to a negative integer such that the accuracy of the result is less than half precision.

Comments

Informational Error

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

Examples

Example 1

In this example, ψ (1.915) is computed and printed.

USE PSI_INT

USE UMACH_INT

IMPLICIT NONE

! Declare variables

INTEGER NOUT

REAL VALUE, X

! Compute

X = 1.915

VALUE = PSI(X)

! Print the results

CALL UMACH (2, NOUT)

WRITE (NOUT,99999) X, VALUE

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

END

Output

PSI( 1.915) = 0.366

Example 2

In this example, ψ (1.9 + 4.3i) is computed and printed.

USE PSI_INT

USE UMACH_INT

IMPLICIT NONE

! Declare variables

INTEGER NOUT

COMPLEX VALUE, Z

! Compute

Z = (1.9, 4.3)

VALUE = PSI(Z)

! Print the results

CALL UMACH (2, NOUT)

WRITE (NOUT,99999) Z, VALUE

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

END

Output

PSI( 1.900, 4.300) = ( 1.507, 1.255)