Rogers–Szegő polynomials

In mathematics, the Rogers–Szegő polynomials are a family of polynomials orthogonal on the unit circle introduced by Szegő (1926), who was inspired by the continuous q-Hermite polynomials studied by Leonard James Rogers. They are given by

where (q;q)n is the descending q-Pochhammer symbol.

Furthermore, the satisfy (for ) the recurrence relation[1]

with and .


  1. Vinroot, C. Ryan (12 July 2012). "An enumeration of flags in finite vector spaces". The Electronic Journal of Combinatorics. 19 (3).
  • Gasper, George; Rahman, Mizan (2004), Basic hypergeometric series, Encyclopedia of Mathematics and its Applications, 96 (2nd ed.), Cambridge University Press, doi:10.2277/0521833574, ISBN 978-0-521-83357-8, MR 2128719
  • Szegő, Gábor (1926), "Beitrag zur theorie der thetafunktionen", Sitz Preuss. Akad. Wiss. Phys. Math. Ki., XIX: 242–252, Reprinted in his collected papers
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.