Big q-Legendre polynomials
Jump to navigation
Jump to search
This article has multiple issues. Please help improve it or discuss these issues on the talk page. (Learn how and when to remove these template messages)
|
In mathematics, the big q-Legendre polynomials are an orthogonal family of polynomials defined in terms of Heine's basic hypergeometric series as[1]
- .
They obey the orthogonality relation
and have the limiting behavior
where is the th Legendre polynomial.[citation needed]
References
- ^ Roelof Koekoek, Peter Lesky, Rene Swattouw, Hypergeometric Orthogonal Polynomials and Their q-Analogues, p 443, Springer