logBeta¶

Evaluates the logarithm of the real beta function $\ln \beta(x,y)$ .

Synopsis¶

logBeta (x, y)

Required Arguments¶

float x (Input): Point at which the logarithm of the beta function is to be evaluated. It must be positive.
float y (Input): Point at which the logarithm of the beta function is to be evaluated. It must be positive.

Return Value¶

The value of the logarithm of the beta function $\beta(x,y)$ .

Description¶

The beta function, $\beta(x,y)$ , is defined to be

$\beta(x,y) = \frac{\mathit{\Gamma}(x)\mathit{\Gamma}(y)}{\mathit{\Gamma}(x+y)} = \int_0^1 t^{x-1} (1-t)^{y-1} dt$

and logBeta returns $\ln \beta(x,y)$ .

The logarithm of the beta function requires that x > 0 and y > 0. It can overflow for very large arguments.

Example¶

Evaluate the log of the beta function $\ln \beta(0.5,0.2)$ .

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

x = 0.5
y = 0.2
ans = logBeta(x, y)
print("logBeta(%f,%f) = %f" % (x, y, ans))

Output¶

logBeta(0.500000,0.200000) = 1.835562

Warning Errors¶

IMSL_X_IS_TOO_CLOSE_TO_NEG_1 The result is accurate to less than one precision because the expression $−x/(x+y)$ is too close to −1.