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

共 30 条

[1] The spherical ensemble and uniform distribution of points on the sphere [J].

Alishahi, Kasra ;

Zamani, Mohammadsadegh .

ELECTRONIC JOURNAL OF PROBABILITY, 2015, 20 :1-27

[2]

Andrews G.E., 1999, ENCY MATH ITS APPL, V71

[3]

[Anonymous], 1878, J MATH PURES APPL

[4]

Beltrán C, 2020, CONSTR APPROX, V52, P283, DOI 10.1007/s00365-020-09506-1

[5] Energy and discrepancy of rotationally invariant determinantal point processes in high dimensional spheres [J].

Beltran, Carlos ;

Marzo, Jordi ;

Ortega-Cerda, Joaquim .

JOURNAL OF COMPLEXITY, 2016, 37 :76-109

[6]

Borodachov S.V., 2019, DISCRETE ENERGY RECT, DOI [DOI 10.1007/978-0-387-84808-2, 10.1007/978-0-387-84808-2]

[7] Hyperuniform point sets on the sphere: probabilistic aspects [J].

Brauchart, Johann S. ;

Grabner, Peter J. ;

Kusner, Woeden ;

Ziefle, Jonas .

MONATSHEFTE FUR MATHEMATIK, 2020, 192 (04) :763-781

[8] A QUANTITATIVE CENTRAL LIMIT THEOREM FOR THE EULER-POINCARE CHARACTERISTIC OF RANDOM SPHERICAL EIGENFUNCTIONS [J].

Cammarota, Valentina ;

Marinucci, Domenico .

ANNALS OF PROBABILITY, 2018, 46 (06) :3188-3228

[9]

Darboux G., 1878, J. Math. Pures Appl, V4, P5

[10]

De Bruijn NG., 1958, ASYMPTOTIC METHODS A

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