besselI1¶

Evaluates the real modified Bessel function of the first kind of order one $I_1(x)$ .

Synopsis¶

besselI1 (x)

Required Arguments¶

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

Return Value¶

The value of the Bessel function

$I_1(x) = \tfrac{1}{\pi} \int_0^{\pi} e^{x \cos \theta} \cos \theta d \theta$

If no solution can be computed, NaN is returned.

Description¶

For large $|x|$ , besselI1 will overflow. It will underflow near zero.

Example¶

The Bessel function $I_1(1.5)$ is evaluated.

from __future__ import print_function
from numpy import *
from pyimsl.math.besselI1 import besselI1

x = 1.5
ans = besselI1(x)
print("I1(%f) = %f" % (x, ans))

Output¶

I1(1.500000) = 0.981666

Alert Errors¶

IMSL_SMALL_ABS_ARG_UNDERFLOW The argument should not be so close to zero that $I_1(x)\approx x/2$ underflows.

Fatal Errors¶

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