psi

Evaluates the derivative of the log gamma function.

Synopsis

psi (x)

Required Arguments

float x (Input)

Argument at which the function is to be evaluated.

Return Values

The value of the derivative of the log gamma function at x. NaN is returned if an error occurs.

Description

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

\[\psi(x) = \frac{d}{dx} \ln \mathit{\Gamma}(x)\]

See gamma for the definition of Γ(x).

The argument x must not be exactly zero or a negative integer, or \(\psi(x)\) 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. If no value can be computed, then NaN is returned.

Example

In this example, \(\psi(1.915)\) is evaluated.

from __future__ import print_function
from numpy import *
from pyimsl.math.psi import psi

x = 1.915
ans = psi(x)
print("psi(%f) = %f" % (x, ans))

Output

psi(1.915000) = 0.366453

Warning Errors

IMSL_NEAR_NEG_INT_WARN

The result is accurate to less than one-half precision because “x” is too close to a negative integer.