Bessel.J Method (Double, Double, Int32)

Evaluate a sequence of Bessel functions of the first kind with real order and real positive argument.

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

Parameters

xnu: A double representing the lowest order desired. xnu must be at least zero and less than 1.
x: A double representing the argument for which the sequence of Bessel functions is to be evaluated.
n: A int representing the order of the last element in the sequence. If order is the highest order desired, set n to int(order).

Return Value

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 + v at x for I=0 to n.

Remarks

The Bessel function , is defined to be

$J_\nu (x) = {{(x/2)^\nu } \over {\sqrt \pi \Gamma (\nu + 1/2)}}\int_0^\pi {\,\,\cos \left( {x\,\cos \,\theta } \right)\sin ^{2\nu } \theta \,\,d\,\theta }$

This code is based on the work of Gautschi (1964) and Skovgaard (1975). It uses backward recursion.

Bessel.J Method (Double, Double, Int32)

Parameters

Return Value

Remarks

See Also