kelvinKer0¶

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

Synopsis¶

kelvinKer0 (x)

Required Arguments¶

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

Return Value¶

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

Description¶

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

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

The function kelvinKer0 is based on the work of Burgoyne (1963). If \(x<0\), NaN (Not a Number) is returned. If \(x\geq 119\), then zero is returned.

Example¶

In this example, \(ker_0(0.4)\) is evaluated.

from __future__ import print_function
from numpy import *
from pyimsl.math.kelvinKer0 import kelvinKer0

x = 0.4
ans = kelvinKer0(x)
print("ker0(0.4) = %f" % (ans))

Output¶

ker0(0.4) = 1.062624