kelvinBei0¶

Evaluates the Kelvin function of the first kind, bei, of order zero.

Synopsis¶

kelvinBei0 (x)

Required Arguments¶

float x (Input): Argument for which the function value is desired.

Return Value¶

The Kelvin function of the first kind, bei, of order zero evaluated at x.

Description¶

The Kelvin function \(bei_0(x)\) is defined to be \(\Im J_0(xe^{3\pi/4})\). The Bessel function \(J_0(x)\) is defined

\[J_0(x) = \tfrac{1}{\pi} \int_0^{\pi} \cos ( x \sin \theta) d \theta\]

The function kelvinBei0 is based on the work of Burgoyne (1963).

In kelvinBei0, x must be less than 119.

Example¶

In this example, \(\text{bei}_0(0.4)\) is evaluated.

from __future__ import print_function
from numpy import *
from pyimsl.math.kelvinBei0 import kelvinBei0

x = 0.4
ans = kelvinBei0(x)
print("bei0(0.4) = %f" % (ans))

Output¶

bei0(0.4) = 0.039998