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
