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. Roelof Koekoek, Peter A. Lesky, and René F. Swarttouw (2010,14) give a detailed list of their properties.

Definition

The polynomials are given in terms of basic hypergeometric functions and the Pochhammer symbol by [1]

p_n(x;a,b,c|q)=\frac{(ab,ac;q)_n}{a^n}*_3\Phi_2(q^-n,ae^{i\theta},ae^{-i\theta};ab,ac|q;q)

In which x=cos(\theta)

Gallery

\displaystyle

References

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