Continuous dual q Hahn polynomials - Alchetron, the free social encyclopedia

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

p n ( x ; a , b , c ∣ q ) = ( a b , a c ; q ) n a n ⋅ 3 Φ 2 ( q − n , a e i θ , a e − i θ ; a b , a c ∣ q ; q )

In which x = cos ⁡ ( θ )

References

Continuous dual q-Hahn polynomials Wikipedia

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