Bessel.I Method (Double, Int32)

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

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

Parameters

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.

The Bessel function

is defined to be

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

The input x must satisfy ${\rm{|x| }} \le {\rm{ log(b) }}$ where b is the largest representable floating-point number. The algorithm is based on a code due to Sookne (1973b), which uses backward recursion.

Bessel.I Method (Double, Int32)

Parameters

Return Value

Remarks

See Also