Weighted $L^2$-Norms of Gegenbauer polynomials

Autor:	Brauchart, Johann S., Grabner, Peter J.
Rok vydání:	2021
Předmět:	Mathematics - Classical Analysis and ODEs Mathematics - Complex Variables Primary 33C45 Secondary 33C20 41A60
Druh dokumentu:	Working Paper
Popis:	We study integrals of the form \begin{equation*} \int_{-1}^1(C_n^{(\lambda)}(x))^2(1-x)^\alpha (1+x)^\beta\, dx, \end{equation*} where $C_n^{(\lambda)}$ denotes the Gegenbauer-polynomial of index $\lambda>0$ and $\alpha,\beta>-1$. We give exact formulas for the integrals and their generating functions, and obtain asymptotic formulas as $n\to\infty$.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2103.08303 Zobrazit plný text záznamu View this record from Arxiv