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Continuous q Hahn polynomials

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Continuous q-Hahn polynomials

In mathematics, the continuous 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 − n e − i n u ( a b e 2 i u , a c , a d ; q ) n ∗ 4 Φ 3 ( q − n , a b c d q n − 1 , a e i ( t + 2 u ) , a e − i t ; a b e 2 i u , a c , a d ; q ; q )

x = c o s ( t + u )

References

Continuous q-Hahn polynomials Wikipedia
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