bessel_exp_I0

Evaluates the exponentially scaled modified Bessel function of the first kind of order zero.

Synopsis

#include <imsl.h>

float imsl_f_bessel_exp_I0 (float x)

The type double function is imsl_d_bessel_exp_I0.

Required Arguments

float x (Input)
Point at which the Bessel function is to be evaluated.

Return Value

The value of the scaled Bessel function e-∣ x∣ I0(x). If no solution can be computed, NaN is returned.

Description

The Bessel function I0(x) is defined to be

 

Example

The expression e-4.5I0 (4.5) is computed directly by calling imsl_f_bessel_exp_I0 and indirectly by calling imsl_f_bessel_I0. The absolute difference is printed. For large x, the internal scaling provided by imsl_f_bessel_exp_I0 avoids overflow that may occur in imsl_f_bessel_I0.

 

#include <imsl.h>

#include <stdio.h>

#include <math.h>

 

int main()

{

float x = 4.5;

float ans;

float error;

 

ans = imsl_f_bessel_exp_I0 (x);

printf("(e**(-4.5))I0(4.5) = %f\n\n", ans);

 

error = fabs(ans - (exp(-x)*imsl_f_bessel_I0(x)));

printf ("Error = %e\n", error);

}

Output

 

(e**(-4.5))I0(4.5) =0.194198

 

Error =4.898845e-09