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Given a elliptic modulus k in an elliptic integral, the modular angle alpha is defined by k=sinalpha. An elliptic integral is written I(phi|m) when the parameter m is used, ...

A composition of a function f degreesf with itself gives a nested function f(f(x)), f degreesf degreesf which gives f(f(f(x)), etc. Function nesting is implemented in the ...

Integrals of the form intf(costheta,sintheta)dtheta (1) can be solved by making the substitution z=e^(itheta) so that dz=ie^(itheta)dtheta and expressing costheta = ...

The following integral transform relationship, known as the Abel transform, exists between two functions f(x) and g(t) for 0<alpha<1, f(x) = int_0^x(g(t)dt)/((x-t)^alpha) (1) ...

The Bessel differential equation is the linear second-order ordinary differential equation given by x^2(d^2y)/(dx^2)+x(dy)/(dx)+(x^2-n^2)y=0. (1) Equivalently, dividing ...

The Hartley Transform is an integral transform which shares some features with the Fourier transform, but which, in the most common convention, multiplies the integral kernel ...

Can be used to invert a Laplace transform.

A linear deconvolution algorithm.

A nonlinear deconvolution technique used in deconvolving images from the Hubble Space Telescope before corrective optics were installed.

An operator definition of a function. A Rodrigues formula may be converted into a Schläfli integral.