besselI0¶

Evaluates the real modified Bessel function of the first kind of order zero $I_0(x)$ .

Synopsis¶

besselI0 (x)

Required Arguments¶

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

Return Value¶

The value of the Bessel function

$I_0(x) = \tfrac{1}{\pi} \int_0^{\pi} \cosh (x \cos \theta) d \theta$

If no solution can be computed, NaN is returned.

Description¶

For large ∣x∣, besselI0 will overflow.

Figure 9.18 — Plot of I0(x) and I1(x)

Example¶

The Bessel function $I_0(1.5)$ is evaluated.

from __future__ import print_function
from numpy import *
from pyimsl.math.besselI0 import besselI0

x = 1.5
ans = besselI0(x)
print("I0(%f) = %f" % (x, ans))

Output¶

I0(1.500000) = 1.646723

Fatal Errors¶

IMSL_LARGE_ABS_ARG_FATAL The absolute value of x must not be so large that $e^{|x|}$ overflows.