Weighted L2-norms of Gegenbauer polynomials

被引：0

作者：

Brauchart, Johann S. ^{[1
]}

Grabner, Peter J. ^{[1
]}

机构：

[1] Graz Univ Technol, Inst Anal & Number Theory, Kopernikusgasse 24-2, A-8010 Graz, Austria

来源：

AEQUATIONES MATHEMATICAE | 2022年 / 96卷 / 04期

基金：

奥地利科学基金会;

关键词：

Gegenbauer polynomials; Hypergeometric functions; Asymptotic analysis; LEGENDRE FUNCTIONS; POWERS;

D O I：

10.1007/s00010-022-00871-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study integrals of the form integral(1)(-1) (C-n((lambda)) (x))(2) (1-x)(alpha) (1+x)(beta) dx, 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 ->infinity.

引用

页码：741 / 762

页数：22

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