Weighted L^2-Norms of Gegenbauer Polynomials --- and more!

Description

I discuss integrals of the form \begin{equation*} \int_{-1}^1(C_n^{(\lambda)}(x))^2(1-x)^\alpha (1+x)^\beta\dd x, \end{equation*} where $C_n^{(\lambda)}$ denotes the Gegenbauer-polynomial of index $\lambda>0$ and $\alpha,\beta>-1$. Such integrals for orthogonal polynomials involving, in particular, a ``wrong'' weight function appear in physics applications and point distribution problems. I present exact formulas for the integrals and their generating functions, and give asymptotic formulas as $n\to\infty$. This is joint work with Peter Grabner also from TU Graz. A preprint of our paper can be found on arXiv.

Period	19 May 2021
Event title	Point Distributions Webinar - Spring 2021
Event type	Seminar
Degree of Recognition	International