Rogers–Szegő polynomials

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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).