Q-Charlier polynomials: Difference between revisions
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In mathematics, the '''''q''-Charlier 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 | url=http://dx.doi.org/10.1007/978-3-642-05014-5 | 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 | id={{MR|2656096}} | year=2010|loc=14}} give a detailed list of their properties. | |||
==Definition== | |||
The polynomials are given in terms of [[basic hypergeometric function]]s and the [[Pochhammer symbol]] by | |||
:<math>\displaystyle </math> | |||
==Orthogonality== | |||
==Recurrence and difference relations== | |||
==Rodrigues formula== | |||
==Generating function== | |||
==Relation to other polynomials== | |||
==References== | |||
*{{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 | id={{MathSciNet | id = 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 | url=http://dx.doi.org/10.1007/978-3-642-05014-5 | 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 | id={{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}} | |||
[[Category:Orthogonal polynomials]] | |||
[[Category:q-analogs]] | |||
[[Category:Special hypergeometric functions]] | |||
Revision as of 01:17, 28 August 2011
In mathematics, the q-Charlier polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Template:Harvs give a detailed list of their properties.
Definition
The polynomials are given in terms of basic hypergeometric functions and the Pochhammer symbol by
- <math>\displaystyle </math>
Orthogonality
Recurrence and difference relations
Rodrigues formula
Generating function
Relation to other polynomials
References
- Gasper, George; Rahman, Mizan (2004), Basic hypergeometric series, 96 (2nd ed.), Cambridge University Press, doi:, Template:MathSciNet, ISBN 978-0-521-83357-8
- Koekoek, Roelof; Lesky, Peter A.; Swarttouw, René F. (2010), Hypergeometric orthogonal polynomials and their q-analogues, Springer-Verlag, doi:, Template:MR, ISBN 978-3-642-05013-8, http://dx.doi.org/10.1007/978-3-642-05014-5
- Template:Dlmf