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.