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The bivariate Rogers–Szegö polynomials

2007
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Journal of Physics A: Mathematical and Theoretical
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We present an operator approach to deriving Mehler's formula and the Rogers formula for the bivariate Rogers-Szegö polynomials h_n(x,y|q). The proof of Mehler's formula can be considered as a new approach to the nonsymmetric Poisson kernel formula for the continuous big q-Hermite polynomials H_n(x;a|q) due to Askey, Rahman and Suslov. Mehler's formula for h_n(x,y|q) involves a _3ϕ_2 sum and the Rogers formula involves a _2ϕ_1 sum. The proofs of these results are based on parameter augmentation

doi:10.1088/1751-8113/40/23/005
fatcat:yvbe6bye6bgyrnseyjxrej5j7a