Bessel.J Method (Double, Int32)

Evaluates a sequence of Bessel functions of the first kind with integer order and real argument.

public static double[] J(
double x,
int n
);

x: A double representing the argument for which the sequence of Bessel functions is to be evaluated.
n: A int which specifies the order of the last element in the sequence.

A double array of length n + 1 containing the values of the function through the series.

Bessel.J[i] contains the value of the Bessel function of order i at x for i = 0 to n.

The Bessel function

, is defined to be

$J_n \left( x \right) = {1 \over \pi }\int_0^\pi {\,\cos \left( {x\,\sin \,\theta - n\,\theta } \right)\,} d\,\theta$

The algorithm is based on a code due to Sookne (1973b) that uses backward recursion with strict error control.