Continuous q-Legendre polynomials

Article
Talk

This article includes inline citations, but they are not properly formatted. Please improve this article by correcting them. (May 2024) (Learn how and when to remove this message)

In mathematics, the continuous q-Legendre polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme.Koekoek, Lesky & Swarttouw (2010) give a detailed list of their properties.^[1]

Definition

The polynomials are given in terms of basic hypergeometric functions by

P_{n}(x|q)={}_{4}\phi _{3}\left(q^{-n},q^{n+1},q^{\frac {1}{4}}e^{i\theta },q^{\frac {1}{4}}e^{-i\theta };q,-q^{-{\frac {1}{2}}},-q;q,q\right),\quad x=\cos \,\theta .

References

^ Koekoek, Roelof; Lesky, Peter A.; Swarttouw, René F. (2010), Hypergeometric orthogonal polynomials and their q-analogues, Springer Monographs in Mathematics, Berlin: Springer-Verlag, p. 14, doi:10.1007/978-3-642-05014-5, ISBN 978-3-642-05013-8, MR 2656096

Sadjang, Patrick Njionou. Moments of Classical Orthogonal Polynomials (Ph.D.). Universität Kassel. CiteSeerX 10.1.1.643.3896.

This polynomial-related article is a stub. You can help Wikipedia by expanding it.

Retrieved from "https://en.wikipedia.org/w/index.php?title=Continuous_q-Legendre_polynomials&oldid=1223601825"