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The Fourier transform of e^(-k_0|x|) is given by F_x[e^(-k_0|x|)](k)=int_(-infty)^inftye^(-k_0|x|)e^(-2piikx)dx = ...

A one-dimensional transform which makes use of the Haar functions.

A fast Fourier transform-like algorithm which produces a hologram of an image.

The forward and inverse Kontorovich-Lebedev transforms are defined by K_(ix)[f(t)] = int_0^inftyK_(ix)(t)f(t)dt (1) K_(ix)^(-1)[g(t)] = ...

Expresses a function in terms of its Radon transform, f(x,y) = R^(-1)(Rf)(x,y) (1) = ...

A one-sided (singly infinite) Laplace transform, L_t[f(t)](s)=int_0^inftyf(t)e^(-st)dt. This is the most common variety of Laplace transform and it what is usually meant by ...

A one-sided (singly infinite) Z-Transform, Z[{a_n}_(n=0)^infty](z)=sum_(n=0)^infty(a_n)/(z^n). This is the most common variety of Z-transform since it is essentially ...

The Hankel transform (of order zero) is an integral transform equivalent to a two-dimensional Fourier transform with a radially symmetric integral kernel and also called the ...

The Mellin transform is the integral transform defined by phi(z) = int_0^inftyt^(z-1)f(t)dt (1) f(t) = 1/(2pii)int_(c-iinfty)^(c+iinfty)t^(-z)phi(z)dz. (2) It is implemented ...

Special functions which arise as solutions to second order ordinary differential equations are commonly said to be "of the first kind" if they are nonsingular at the origin, ...