The Bivariate Rogers-Szegö Polynomials

  title={The Bivariate Rogers-Szeg{\"o} Polynomials},
  author={William Y. C. Chen and Husam L. Saad and Lisa Hui Sun},
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

From This Paper

Topics from this paper.


Publications referenced by this paper.
Showing 1-10 of 25 references

A q-umbral calculus

  • E. C. Ihrig, M.E.H. Ismail
  • J. Math. Anal. Appl. 84
  • 1981
Highly Influential
8 Excerpts

Two operator identities and their applications to terminating basic hypergeometric series and q-integrals

  • Z. Z. Zhang, J. Wang
  • J. Math. Anal. Appl. 312
  • 2005
Highly Influential
3 Excerpts

The homogeneous q-difference operator

  • W.Y.C. Chen, A. M. Fu, B. Y. Zhang
  • Adv. Appl. Math. 31
  • 2003
Highly Influential
7 Excerpts

Combinatorial Enumeration

  • I. P. Goulden, D. M. Jackson
  • John Wiley, New York
  • 1983
Highly Influential
3 Excerpts

Fourier-Gauss transforms of the continuous big q-Hermite polynomials

  • M. K. Atakishiyeva, N. M. Atakishiyev
  • J. Phys. A: Math. Gen. 30
  • 1997
1 Excerpt

Similar Papers

Loading similar papers…