Special functions

CCATSL provides routines for evaluating three standard mathematical functions, BesselCL for Bessel functions of the first kind of integer order, PhiCL for the normal distribution function and InvPhiCL for its inverse.

Bessel function of first kind, BesselCL

BesselCL computes the Bessel function of the first kind, $J_n(x)$ for $n$ a positive integer, which may be defined by

$$\m J_n(x)=\sum_{k=0}^{\infty}\frac{(-1)^k\bigl(\frac{1}{2}x\bigr)^{2k+n}}{k!\,(n+k)!}.$$

	double BesselCL (	int n,
		double x);

	n		Specifies the order $n$ of the required Bessel function.
	x		Specifies the argument to $J_n$.

The return value is an accurate approximation to $J_n(x)$.

Normal distribution function, PhiCL

PhiCL computes the normal distribution function, defined by

$$\m \Phi(x)=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^x \exp(-\textstyle\frac{1}{2}u^2)\,du$$

	double PhiCL (	double x);

x

Specifies the argument to $\Phi$.

The return value is an accurate approximation to $\Phi(x)$.

Inverse cumulative normal density function, InvPhiCL

InvPhiCL computes $\Phi^{-1}(x)$, the inverse function to $\Phi(x)$, the normal distribution function.

	double InvPhiCL (	double x);

x

Specifies the argument to $\Phi^{-1}$.

The return value is an accurate approximation to $\Phi^{-1}(x)$.