“Big q-Jacobi polynomials”的意思、由来-开放百科全书

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Big q-Jacobi polynomials

释义

Definition
References

In mathematics, the big q-Jacobi polynomials P_n(x;a,b,c;q), introduced by {{harvtxt|Andrews|Askey|1985}}, are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. {{harvs|txt | 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|loc=14}} give a detailed list of their properties.

Definition

The polynomials are given in terms of basic hypergeometric functions by

References

{{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}}
{{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 | doi=10.2277/0521833574 | 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}}
{{dlmf|id=18|title=|first=Tom H. |last=Koornwinder|first2=Roderick S. C.|last2= Wong|first3=Roelof |last3=Koekoek||first4=René F. |last4=Swarttouw}}

3 : Orthogonal polynomials|Q-analogs|Special hypergeometric functions

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