## Some systems of multivariable orthogonal $$q$$-Racah polynomials.(English)Zbl 1121.33019

The authors employ certain $$q$$-identities and $$q$$-summation formulae, for example, summation formula for terminating $${_6\phi_5}$$ to derive basic analogs of extended Racah polynomials and second system of Racah’s multivariate orthogonal polynomials as considered by M. V. Tratnik [J. Math. Phys. 32, No. 9, 2337–2342 (1991; Zbl 0742.33007)]. Special and limit cases of their results provide interesting known results.

### MSC:

 33D50 Orthogonal polynomials and functions in several variables expressible in terms of basic hypergeometric functions in one variable 33D45 Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) 33D15 Basic hypergeometric functions in one variable, $${}_r\phi_s$$

Zbl 0742.33007
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### References:

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