Big q-Jacobi polynomials
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In mathematics, the big q-Jacobi polynomials Pn(x;a,b,c;q) are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme.{{citation |last1=Andrews |first1=George E. |authorlink1=George Andrews (mathematician)| last2=Askey |first2=Richard |authorlink2=Richard Askey |editor1-last=Brezinski |editor1-first=C. |editor2-last=Draux |editor2-first=A. |editor3-last=Magnus |editor3-first=Alphonse P. |editor4-last=Maroni |editor4-first=Pascal |editor5-last=Ronveaux |editor5-first=A. |title=Polynômes orthogonaux et applications. Proceedings of the Laguerre symposium held at Bar-le-Duc, October 15–18, 1984. |publisher=Springer-Verlag |location=Berlin, New York |series=Lecture Notes in Math |isbn=978-3-540-16059-5 |mr=838970 |year=1985 |volume=1171 |chapter=Classical orthogonal polynomials |doi=10.1007/BFb0076530 |pages=36–62}}
Definition
The polynomials are given in terms of basic hypergeometric functions by
:
References
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Further reading
- {{citation |last1=Gasper |first1=George |last2=Rahman |first2=Mizan |title=Basic hypergeometric series |publisher=Cambridge University Press |edition=2nd |series=Encyclopedia of Mathematics and its Applications |isbn=978-0-521-83357-8 |mr=2128719 |year=2004 |volume=96}}
- {{citation |last1=Koekoek |first1=Roelof |last2=Lesky |first2=Peter A. |last3=Swarttouw |first3=René F. |title=Hypergeometric orthogonal polynomials and their q-analogues |publisher=Springer-Verlag |location=Berlin, New York |series=Springer Monographs in Mathematics |isbn=978-3-642-05013-8 |doi=10.1007/978-3-642-05014-5 |mr=2656096 |year=2010 | contribution = 9.8 Jacobi | pages = 216–221}} gives a detailed list of properties.
- {{dlmf|id=18|title=Chapter 18: Orthogonal Polynomials |first=Tom H. |last=Koornwinder |first2=Roderick S. C. |last2=Wong |first3=Roelof |last3=Koekoek |first4=René F. |last4=Swarttouw}}
Category:Orthogonal polynomials
Category:Special hypergeometric functions
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