Q-Charlier polynomials: Difference between revisions

Revision as of 12:21, 21 February 2021

In mathematics, the q-Charlier polynomials^[1] are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Template:Harvs give a detailed list of their properties.

The polynomials are given in terms of the basic hypergeometric function by

<math>\displaystyle C_n(q^{-x};a;q) = {}_2\phi_1(q^{-n},q^{-x};0;q,-q^{n+1}/a).</math>

Gasper, George; Rahman, Mizan (2004), Basic hypergeometric series, 96 (2nd ed.), Cambridge University Press, doi:10.2277/0521833574, 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:10.1007/978-3-642-05014-5, ISBN 978-3-642-05013-8
Template:Dlmf
Template:Cite thesis

↑ There are similar named polynomials named alternative q-Charlier polynomials <math>K_n(x;a;q)</math>.

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 {{DISPLAYTITLE:''q''-Charlier polynomials }}
-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 | 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.
+In mathematics, the '''''q''-Charlier polynomials'''<ref>There are similar named polynomials named  alternative q-Charlier polynomials <math>K_n(x;a;q)</math>.</ref> 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==