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Any computable function can be incorporated into a program using while-loops (i.e., "while something is true, do something else"). For-loops (which have a fixed iteration ...

The elliptic exponential function eexp_(a,b)(u) gives the value of x in the elliptic logarithm eln_(a,b)(x)=1/2int_infty^x(dt)/(sqrt(t^3+at^2+bt)) for a and b real such that ...

A generalized hypergeometric function _pF_q(a_1,...,a_p;b_1,...,b_q;x) is a function which can be defined in the form of a hypergeometric series, i.e., a series for which the ...

The interesting function defined by the definite integral G(x)=int_0^xsin(tsint)dt, illustrated above (Glasser 1990). The integral cannot be done in closed form, but has a ...

Any real function u(x,y) with continuous second partial derivatives which satisfies Laplace's equation, del ^2u(x,y)=0, (1) is called a harmonic function. Harmonic functions ...

The Cunningham function, sometimes also called the Pearson-Cunningham function, can be expressed using Whittaker functions (Whittaker and Watson 1990, p. 353). ...

The Blancmange function, also called the Takagi fractal curve (Peitgen and Saupe 1988), is a pathological continuous function which is nowhere differentiable. Its name ...

Let c and d!=c be real numbers (usually taken as c=1 and d=0). The Dirichlet function is defined by D(x)={c for x rational; d for x irrational (1) and is discontinuous ...

The apodization function f(x)=1-(|x|)/a (1) which is a generalization of the one-argument triangle function. Its full width at half maximum is a. It has instrument function ...

A folding function is a function that maps the integers Z={...,-3,-2,-1,0,1,2,3,...} onto the nonnegative integers Z^*={0,1,2,3,...}. This type of function arises naturally ...