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The function [x] which gives the smallest integer >=x, shown as the thick curve in the above plot. Schroeder (1991) calls the ceiling function symbols the "gallows" because ...

A function whose value decreases to zero more slowly than any nonzero polynomial is said to be a logarithmically decreasing function. The prototypical example is the function ...

A function whose value increases more slowly to infinity than any nonconstant polynomial is said to be a logarithmically increasing function. The prototypical example is the ...

The finite Fourier cosine transform of an apodization function, also known as an apparatus function. The instrument function I(k) corresponding to a given apodization ...

The Dedekind eta function is defined over the upper half-plane H={tau:I[tau]>0} by eta(tau) = q^_^(1/24)(q^_)_infty (1) = q^_^(1/24)product_(k=1)^(infty)(1-q^_^k) (2) = ...

Let f(x) be differentiable on the open interval (a,b) and continuous on the closed interval [a,b]. Then there is at least one point c in (a,b) such that ...

A boundary value problem is a problem, typically an ordinary differential equation or a partial differential equation, which has values assigned on the physical boundary of ...

An initial value problem is a problem that has its conditions specified at some time t=t_0. Usually, the problem is an ordinary differential equation or a partial ...

By analogy with the sinc function, define the tanc function by tanc(z)={(tanz)/z for z!=0; 1 for z=0. (1) Since tanz/z is not a cardinal function, the "analogy" with the sinc ...

A function which arises in the fractional integral of e^(at), given by E_t(nu,a) = (e^(at))/(Gamma(nu))int_0^tx^(nu-1)e^(-ax)dx (1) = (a^(-nu)e^(at)gamma(nu,at))/(Gamma(nu)), ...