Continuous q-Legendre polynomials
From HandWiki
In mathematics, the continuous q-Legendre polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme.(Koekoek Lesky) give a detailed list of their properties.[1]
Definition
The polynomials are given in terms of basic hypergeometric functions by
- [math]\displaystyle{ P_{n}(x|q)={}_4\phi_3\left(q^{-n},q^{n+1},q^{\frac14}e^{i\theta},q^{\frac14}e^{-i\theta};q,-q^{-\frac12},-q;q,q\right),\quad x=\cos\,\theta. }[/math]
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
- Sadjang, Patrick Njionou. Moments of Classical Orthogonal Polynomials (Ph.D.). Universität Kassel. CiteSeerX 10.1.1.643.3896.
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