PSI1

This function evaluates the second derivative of the log gamma function.

Function Return Value

PSI1 — Function value. (Output)

Required Arguments

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

FORTRAN 90 Interface

Generic: PSI1 (X)

Specific: The specific interface names are S_PSI1 and D_PSI1.

Description

The psi1 function, also called the trigamma 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 ψ1(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 PSI1(X) is accurate to less than one‑half precision because X is too near a negative integer.

Example

In this example, ψ1(1.915) is computed and printed.

 

USE PSI1_INT

USE UMACH_INT

 

IMPLICIT NONE

! Declare variables

INTEGER NOUT

REAL VALUE, X

! Compute

X = 1.915

VALUE = PSI1(X)

! Print the results

CALL UMACH (2, NOUT)

WRITE (NOUT,99999) X, VALUE

99999 FORMAT (' PSI1(', F6.3, ') = ', F6.3)

END

Output

 

PSI1( 1.915) = 0.681