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The Fourier transform is a generalization of the complex Fourier series in the limit as L->infty. Replace the discrete A_n with the continuous F(k)dk while letting n/L->k. ...

A tiling consisting of a rhombus such that 17 rhombuses fit around a point and a second tile in the shape of six rhombuses stuck together. These two tiles can fill the plane ...

Householder (1953) first considered the matrix that now bears his name in the first couple of pages of his book. A Householder matrix for a real vector v can be implemented ...

If, after constructing a difference table, no clear pattern emerges, turn the paper through an angle of 60 degrees and compute a new table. If necessary, repeat the process. ...

Jonquière's relation, sometimes also spelled "Joncquière's relation" (Erdélyi et al. 1981, p. 31), states ...

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 ...

Let A be an involutive algebra over the field C of complex numbers with involution xi|->xi^♯. Then A is a left Hilbert algebra if A has an inner product <·,·> satisfying: 1. ...

If a function has a Fourier series given by f(x)=1/2a_0+sum_(n=1)^inftya_ncos(nx)+sum_(n=1)^inftyb_nsin(nx), (1) then Bessel's inequality becomes an equality known as ...

A group theoretic operation which is useful in the study of complex atomic spectra. A plethysm takes a set of functions of a given symmetry type {mu} and forms from them ...

A principal nth root omega of unity is a root satisfying the equations omega^n=1 and sum_(i=0)^(n-1)omega^(ij)=0 for j=1, 2, ..., n. Therefore, every primitive root of unity ...