q-Charlier polynomials

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 q-Charlier polynomials are given in terms of the basic hypergeometric function by

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

Relation to other polynomials

Template:Empty section Q-Charlier polynomials →Charlier polynomials

Gallery

Q-CHARLIER ABS COMPLEX 3D MAPLE PLOT

File:Q-CHARLIER IM COMPLEX 3D MAPLE PLOT.gif Q-CHARLIER IM COMPLEX 3D MAPLE PLOT

File:Q-CHARLIER RE COMPLEX 3D MAPLE PLOT.gif Q-CHARLIER RE COMPLEX 3D MAPLE PLOT

File:Q-CHARLIER ABS DENSITY MAPLE PLOT.gif Q-CHARLIER ABS DENSITY MAPLE PLOT

File:Q-CHARLIER IM DENSITY MAPLE PLOT.gif Q-CHARLIER IM DENSITY MAPLE PLOT

File:Q-CHARLIER RE DENSITY MAPLE PLOT.gif Q-CHARLIER RE DENSITY MAPLE PLOT

References

• 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 
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