kelvinKei0¶

Evaluates the Kelvin function of the second kind, kei, of order zero.

Synopsis¶

kelvinKei0 (x)

Required Arguments¶

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

Return Value¶

The Kelvin function of the second kind, kei, of order zero evaluated at x.

Description¶

The modified Kelvin function $\text{kei}_0(x)$ is defined to be $\Im K_0(xe^{\pi/4})$ . The Bessel function $K_0(x)$ is defined

$K_0(x) = \int_0^{\infty} \cos (x \sin t) dt$

The function kelvinKei0 is based on the work of Burgoyne (1963). If $x<0$ , NaN (Not a Number) is returned. If $x\geq 119$ , zero is returned.

Example¶

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

from __future__ import print_function
from numpy import *
from pyimsl.math.kelvinKei0 import kelvinKei0

x = 0.4
ans = kelvinKei0(x)
print("kei0(0.4) = %f" % (ans))

Output¶

kei0(0.4) = -0.703800