Continuous dual q-Hahn polynomials explained

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 ^[1]

p _{n(x;a,b,c\mid} q) = ((ab,ac;q) _{n})/(a ^{n}) { _{3\phi} ^{- n} ^{2 }(q} ,ae ^{i\theta} ,ae ^{-i\theta} ; ab, ac \mid q;q)

In which

x = \cos(\theta)

Notes and 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