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Continuous dual q-Hahn polynomials

In mathematics, the continuous dual q-Hahn polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. give a detailed list of their properties.

Definition

The polynomials are given in terms of basic hypergeometric functions and the q-Pochhammer symbol by

: p_n(x;a,b,c\mid q)=\frac{(ab,ac;q)_n}{a^n}{_3\phi_2}(q^{-n},ae^{i\theta},ae^{-i\theta}; ab, ac \mid q;q)

In which x=\cos(\theta)

Gallery

[[File:Continuous dual qHahn function abs complex3D Maple PLOT.gif	thumb]]	[[File:Continuous dual qHahn function re complex3D Maple PLOT.gif	thumb]]	[[File:Continuous dual qHahn function Im complex3D Maple PLOT.gif	thumb]]

[[File:Continuous dual qHahn function RE density Maple PLOT.gif	thumb]]	[[File:Continuous dual qHahn function Im density Maple PLOT.gif	thumb]]	[[File:Continuous dual qHahn function ABS density Maple PLOT.gif	thumb]]

References

Mesuma Atakishiyeva, Natig Atakishieyev, A NON STANDARD GENERATING FUNCTION FOR CONTINUOUS DUAL Q-HAHN POLYNOMIALS, REVISTA DE MATEMATICA 2011 18(1):111-120

Wikipedia Source

This article was imported from Wikipedia and is available under the Creative Commons Attribution-ShareAlike 4.0 License. Content has been adapted to SurfDoc format. Original contributors can be found on the article history page.

orthogonal-polynomials q-analogs special-hypergeometric-functions

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