The Bivariate Rogers-Szegö Polynomials

@inproceedings{Chen2006TheBR,
  title={The Bivariate Rogers-Szeg{\"o} Polynomials},
  author={William Y. C. Chen and Husam L. Saad and Lisa Hui Sun},
  year={2006}
}
We obtain Mehler’s formula and the Rogers formula for the continuous big qHermite polynomials Hn(x; a|q). Instead of working with the polynomials Hn(x; a|q) directly, we consider the equivalent forms in terms of the bivariate Rogers-Szegö polynomials hn(x, y|q) recently introduced by Chen, Fu and Zhang. It turns out that Mehler’s formula for Hn(x; a|q) involves a 3φ2 sum, and the Rogers formula involves a 2φ1 sum. The proofs of these results are based on parameter augmentation with respect to… CONTINUE READING

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