Moments of q-Jacobi Polynomials and q-Zeta Values

TL;DR

This paper investigates the relationships between q-Jacobi polynomial moments, q-analogues of Dirichlet series at negative integers, and q-Eulerian polynomials associated with wreath products of symmetric groups.

Contribution

It uncovers new connections linking q-Jacobi polynomial moments with q-analogues of Dirichlet series and q-Eulerian polynomials, expanding understanding of their interplay.

Findings

Identified explicit formulas connecting moments of q-Jacobi polynomials and q-Dirichlet series.

Established new relationships between q-Eulerian polynomials and polynomial moments.

Provided insights into the algebraic structures underlying these q-analogues.

Abstract

We explore some connections between moments of rescaled little q-Jacobi polynomials, q-analogues of values at negative integers for some Dirichlet series, and the q-Eulerian polynomials of wreath products of symmetric groups.