function BesselI0(X: Double): Double;
Zeroth-order modified Bessel function of the first kind.
| # | Name | Type | Description |
|---|---|---|---|
| 1 | X | Double | scalar |
Returns: Double
Remarks:
Returns I_0(X), the modified Bessel function of the first kind of order zero, evaluated by the convergent power series
I_0(X) = sum_(k=0)^(inf) 1/(k!)^2(X/2)^(2k)
It is even (I_0(-X)=I_0(X)), real, and grows like e^(|X|)/sqrt(2pi|X|) for large |X|; I_0(0)=1. This is the kernel of the Kaiser window (see Kaiser). Domain: any finite real X (the series is summed until the increment falls below machine epsilon). Returns a finite double for finite X; very large |X| overflows to +inf rather than raising.
References:
[1] Discrete-time signal processing, Oppenheim and Schafer, Prentice-Hall, 1989.