Askey–Wilson polynomials — In mathematics, the Askey Wilson polynomials are the polynomials:p n(x;a,b,c|q) =(ab,ac,ad;q) na^{ n}; {4}phi 3 left [egin{matrix} q^{ n} abcdq^{n 1} ae^{i heta} ae^{ i heta} ab ac ad end{matrix} ; q,q ight] where phi; is a basic hypergeometric… … Wikipedia
Orthogonal polynomials — In mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonal to each other under some inner product. The most widely used orthogonal polynomials are the… … Wikipedia
Macdonald polynomials — In mathematics, Macdonald polynomials Pλ(x; t,q) are a family of orthogonal polynomials in several variables, introduced by Macdonald (1987). Macdonald originally associated his polynomials with weights λ of finite root systems and used just … Wikipedia
Koornwinder polynomials — In mathematics, Koornwinder polynomials are a family of orthogonal polynomials in several variables, named for their discoverer Tom H. Koornwinder, that generalize the Askey Wilson polynomials. They can also be viewed as Macdonald polynomials… … Wikipedia
Continuous Hahn polynomials — In mathematics, the continuous Hahn polynomials are a family of orthogonal polynomials in the Askey scheme of hypergeometric orthogonal polynomials. They are defined in terms of generalized hypergeometric functions by Roelof Koekoek, Peter A.… … Wikipedia
Continuous dual Hahn polynomials — In mathematics, the continuous dual Hahn polynomials are a family of orthogonal polynomials in the Askey scheme of hypergeometric orthogonal polynomials. They are defined in terms of generalized hypergeometric functions by Roelof Koekoek, Peter A … Wikipedia
Charlier polynomials — In mathematics, Charlier polynomials (also called Poisson–Charlier polynomials) are a family of orthogonal polynomials introduced by Carl Charlier. They are given in terms of the generalized hypergeometric function by where L are Laguerre… … Wikipedia
Hahn polynomials — In mathematics, the Hahn polynomials are a family of orthogonal polynomials introduced by harvtxt|Hahn|1949. They are defined in terms of hypergeometric functions by :Q n(x;a,b,N)= {} 3F 2( n, x,n+a+b+1;a+1, N+1;1). ee also*Wilson polynomials, a… … Wikipedia
Racah polynomials — In mathematics, Racah polynomials are orthogonal polynomials named after Giulio Racah, as their orthogonality relations are equivalent to his orthogonality relations for Racah coefficients.The Racah polynomials were first defined by… … Wikipedia
Continuous q-Jacobi polynomials — In mathematics, the continuous q Jacobi polynomials P(α,β) n(x|q), introduced by Askey Wilson (1985), are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek, Peter A. Lesky, and René F.… … Wikipedia
