- Definition
- Orthogonality
- Recurrence and difference relations
- Rodrigues formula
- Generating function
- Relation to other polynomials
- Gallery
- References
In mathematics, the q-Bessel polynomials 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 and the Pochhammer symbol by [1]：
Orthogonality
[2]Recurrence and difference relations
{{Empty section|date=September 2011}}Rodrigues formula
{{Empty section|date=September 2011}}Generating function
{{Empty section|date=September 2011}}Relation to other polynomials
{{Empty section|date=September 2011}}Gallery
References
1. ^Roelof Koekoek, Peter Lesky Rene Swarttouw,Hypergeometric Orthogonal Polynomials and their q-Analogues, p526 Springer 2010
2. ^Roelof p527
2. ^Roelof p527
- {{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=Orthogonal Polynomials|first1=Tom H. |last1=Koornwinder|first2=Roderick S. C.|last2= Wong|first3=Roelof |last3=Koekoek||first4=René F. |last4=Swarttouw|url=http://dlmf.nist.gov/18|archive-url=http://dlmf.nist.gov/18}}
3 : Orthogonal polynomials|Q-analogs|Special hypergeometric functions
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