Harman Patil (Editor)

Q Racah polynomials

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In mathematics, the q-Racah polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme, introduced by Askey & Wilson (1979). Roelof Koekoek, Peter A. Lesky, and René F. Swarttouw (2010, 14) give a detailed list of their properties.

Contents

Definition

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

p n ( q − x + q x + 1 c d ; a , b , c , d ; q ) = 4 ϕ 3 [ q − n a b q n + 1 q − x q x + 1 c d a q b d q c q ; q ; q ]

They are sometimes given with changes of variables as

W n ( x ; a , b , c , N ; q ) = 4 ϕ 3 [ q − n a b q n + 1 q − x c q x − n a q b c q q − N ; q ; q ]

Relation to other polynomials

q-Racah polynomials→Racah polynomials

References

Q-Racah polynomials Wikipedia
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