# 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 .

## References

- 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

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