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Q-Racah polynomials
In mathematics, the q-Racah polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme, introduced by . 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(q^{-x}+q^{x+1}cd;a,b,c,d;q) = {}_4\phi_3\left[\begin{matrix} q^{-n} &abq^{n+1}&q^{-x}&q^{x+1}cd\ aq&bdq&cq\ \end{matrix};q;q\right] They are sometimes given with changes of variables as :W_n(x;a,b,c,N;q) = {}_4\phi_3\left[\begin{matrix} q^{-n} &abq^{n+1}&q^{-x}&cq^{x-n}\ aq&bcq&q^{-N}\ \end{matrix};q;q\right]
Relation to other polynomials
q-Racah polynomials→Racah polynomials
References
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