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The inverse of the Laplace transform, given by F(t)=1/(2pii)int_(gamma-iinfty)^(gamma+iinfty)e^(st)f(s)ds, where gamma is a vertical contour in the complex plane chosen so ...

A Maclaurin series is a Taylor series expansion of a function about 0, (1) Maclaurin series are named after the Scottish mathematician Colin Maclaurin. The Maclaurin series ...

The spherical harmonics form a complete orthogonal system, so an arbitrary real function f(theta,phi) can be expanded in terms of complex spherical harmonics by ...

A region in a knot or link projection plane surrounded by a circle such that the knot or link crosses the circle exactly four times. Two tangles are equivalent if a sequence ...

If it is possible to transform a coordinate system to a form where the metric elements g_(munu) are constants independent of x^mu, then the space is flat.

The Cesàro means of a function f are the arithmetic means sigma_n=1/n(s_0+...+s_(n-1)), (1) n=1, 2, ..., where the addend s_k is the kth partial sum ...

There are two sets of constants that are commonly known as Lebesgue constants. The first is related to approximation of function via Fourier series, which the other arises in ...

Riddell's formula for unlabeled graphs is the Euler transform relating the number of unlabeled connected graphs on n nodes satisfying some property with the corresponding ...

A substitution which can be used to transform integrals involving square roots into a more tractable form. form substitution sqrt(x^2+a^2) x=asinhu sqrt(x^2-a^2) x=acoshu

The function K(alpha,t) in an integral or integral transform g(alpha)=int_a^bf(t)K(alpha,t)dt. Whittaker and Robinson (1967, p. 376) use the term nucleus for kernel.