log_beta

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

Synopsis

#include <imsl.h>

float imsl_f_log_beta (float x, float y)

The type double function is imsl_d_log_beta.

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 β(x, y).

Description

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

 

and imsl_f_log_beta returns ln β(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 β(0.5, 0.2).

 

#include <imsl.h>

#include <stdio.h>

 

int main()

{

float x = 0.5;

float y = 0.2;

float ans;

 

ans = imsl_f_log_beta(x, y);

printf("log beta(%f,%f) = %f\n", x, y, ans);

}

Output

 

log beta(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.