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Let there be two particularly well-behaved functions F(x) and p_tau(x). If the limit lim_(tau->0)int_(-infty)^inftyp_tau(x)F(x)dx exists, then p_tau(x) is a regular sequence ...

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

The Schur polynomials are a class of orthogonal polynomials. They are a special case of the Jack polynomials corresponding to the case alpha=1.

psi=(A_0+alpha_1A_1+alpha_2A_2+...)e^(iS/alpha).

Solving the wave equation on a disk gives a solution in terms of Bessel functions.

A function w(x) used to normalize orthogonal functions int[f_n(x)]^2w(x)dx=N_n.

The polynomials a_n^((beta))(x) given by the Sheffer sequence with g(t) = (1-t)^(-beta) (1) f(t) = ln(1-t), (2) giving generating function ...

An affine tensor is a tensor that corresponds to certain allowable linear coordinate transformations, T:x^_^i=a^i_jx^j, where the determinant of a^i_j is nonzero. This ...

A polynomial sequence p_n(x) is called the basic polynomial sequence for a delta operator Q if 1. p_0(x)=1, 2. p_n(0)=0 for all n>0, 3. Qp_n(x)=np_(n-1)(x). If p_n(x) is a ...

If f(x) is piecewise continuous and has a generalized Fourier series sum_(i)a_iphi_i(x) (1) with weighting function w(x), it must be true that ...