Bessel.I Method (Double, Double, Int32)

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

public static double[] I(
   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 of the Bessel functions to be evaluated.
n: The int order of the last element in the sequence.

Return Value

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

Remarks

Bessel.I[i] contains the value of the Bessel function of order i+xnu.

The Bessel function

, is defined to be

$I_\nu (x) = {1 \over \pi }\int_0^\pi {e^{x\cos \theta } } \cos (\nu \theta )d\,\theta - {{\sin (\nu \pi )} \over \pi }\int_0^\infty {e^{ - x\cosh t - vt} } dt$

Here, argument xnu is represented by $\nu$ in the above equation.

The input x must be nonnegative and less than or equal to log(b) (b is the largest representable number). The argument $\nu$ = xnu must satisfy ${\rm{0 }} \le {\rm{ }}\nu {\rm{ }} \le {\rm{ 1}}$ .

This function is based on a code due to Cody (1983), which uses backward recursion.

Bessel.I Method (Double, Double, Int32)

Parameters

Return Value

Remarks

See Also