Q-Charlier polynomials: Difference between revisions
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The polynomials are given in terms of the [[basic hypergeometric function]] by | 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> | :<math>\displaystyle C_n(q^{-x};a;q) = {}_2\phi_1(q^{-n},q^{-x};0;q,-q^{n+1}/a).</math> | ||
==References== | ==References== | ||
Revision as of 06:55, 14 May 2022
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.
Definition
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>
References
- ↑ There are similar named polynomials named alternative q-Charlier polynomials <math>K_n(x;a;q)</math> which is another name for q-Bessel polynomials.
- Gasper, George; Rahman, Mizan (2004), Basic hypergeometric series, 96 (2nd ed.), Cambridge University Press, doi:, 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:, ISBN 978-3-642-05013-8
- Template:Dlmf
- Template:Cite thesis