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Big q Jacobi polynomials

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In mathematics, the big q-Jacobi polynomials Pn(x;a,b,c;q), introduced by Andrews & Askey (1985), 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 by

P n ( x ; a , b , c ; q ) = 3 ϕ 2 ( q − n , a b q n + 1 , x ; a q , c q ; q , q )

References

Big q-Jacobi polynomials Wikipedia
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