Wilson polynomials

From Wikipedia, the free encyclopedia

In mathematics, Wilson polynomials are a family of orthogonal polynomials introduced by James A. Wilson (1980) that generalize Jacobi polynomials, Hahn polynomials, and Charlier polynomials.

$p_{n}(t^{2})=(a+b)_{n}(a+c)_{n}(a+d)_{n}{}_{4}F_{3}\left({\begin{matrix}-n&a+b+c+d+n-1&a-t&a+t\\a+b&a+c&a+d\end{matrix}};1\right).$

References

Wilson, James A. (1980), "Some hypergeometric orthogonal polynomials", SIAM Journal on Mathematical Analysis 11 (4): 690–701, doi:10.1137/0511064, ISSN 0036-1410, MR 579561
Koornwinder, T.H. (2001), "Wilson polynomials", in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4

This article is issued from Wikipedia. The text is available under the Creative Commons Attribution/Share Alike; additional terms may apply for the media files.