Some Functions in the library

Several types of functions have been implemented in this scheme. A table of those functions is shown here. Certain functions, such as Legendre Polynomials, take arguments to their constructor that specify the order of the polynomial. In other cases internal parameters govern the shape of the function. The distinction is arbitrary at times, since, for example, Bessel functions need not be of integral order. In general we have preferred to leave parameters out of functions if one can obtain the same result by other means, for example, objects of class Sin do not have a frequency parameter since one can obtain this as follows:

Parameter freq (``freq'', 10.0);	
Sin sine;
Variable x;	
GENFUNCTION f = sine(freq*x);

Function	Name	Parameters
Variable	Returns its own input
FixedConstant	Returns a constant
Sqrt	Sqrt
Square	Returns square of input
Power	Returns a power of input
Exp	Exponential
Sin	Sine
Cos	Cosine
Tan	Tangent
Ln	Natural Logarithm
Erf	Error function
ForwardExp	Forward Exponentail tail	decayConstant
ReverseExp	Reverse Exponential tail	decayConstant
LogGamma	Natural log of Gamma function
IncompleteGamma	Incomplete Gamma Function	a
CumulativeChiSquare	Probability($\chi^2$)
Gauss	Gaussian (Normal) distribution	mean
		sigma
Landau	Landau distribution	peak
		width
Rectangular	Rectangular function	x0
		x1
		baseline
		height
PeriodicRectangular	Periodic rectangular	spacing
		width
		height
SphericalBessel	Spherical Bessel Functions
SphericalNeumann	Spherical Neumann Function
AssociatedLaguerre	Associated Laguerre Polynomial
AssociatedLegendre	Associated Legendre Polynomial
AnalyticConvolution	Moser-Roussarie convolutions	frequency
		lifetime
		resolution
IntegralOrder::Bessel	Bessel and Neumann functions
FractionalOrder::Bessel	Bessel and Neumann functions	order
BivariateGaussian	Gaussian in 2 variables	mean0, mean1,
		sigma0,sigma1, corr01
TrivariateGaussian	Gaussian in 3 variables	mean[0-2],sigma[0-2]
		corr[0-2][0-2]