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A special case of the quadratic Diophantine equation having the form x^2-Dy^2=1, (1) where D>0 is a nonsquare natural number (Dickson 2005). The equation x^2-Dy^2=+/-4 (2) ...

The permanent is an analog of a determinant where all the signs in the expansion by minors are taken as positive. The permanent of a matrix A is the coefficient of x_1...x_n ...

The word quadrature has (at least) three incompatible meanings. Integration by quadrature either means solving an integral analytically (i.e., symbolically in terms of known ...

A method for finding recurrence relations for hypergeometric polynomials directly from the series expansions of the polynomials. The method is effective and easily ...

A symmetric polynomial on n variables x_1, ..., x_n (also called a totally symmetric polynomial) is a function that is unchanged by any permutation of its variables. In other ...

A transpose of a doubly indexed object is the object obtained by replacing all elements a_(ij) with a_(ji). For a second-tensor rank tensor a_(ij), the tensor transpose is ...

Angle addition formulas express trigonometric functions of sums of angles alpha+/-beta in terms of functions of alpha and beta. The fundamental formulas of angle addition in ...

A connection on a vector bundle pi:E->M is a way to "differentiate" bundle sections, in a way that is analogous to the exterior derivative df of a function f. In particular, ...

A weakly binary tree is a planted tree in which all nonroot graph vertices are adjacent to at most three graph vertices. Let g(z)=sum_(i=0)^inftyg_iz^i, (1) be the generating ...

The Wiener-Hopf method is a powerful technique which enables certain linear partial differential equations subject to boundary conditions on semi-infinite domains to be ...