Expressing Sums of Finite Products of Chebyshev Polynomials of the Second Kind and of Fibonacci Polynomials by Several Orthogonal Polynomials

被引：3

作者：

Kim, Taekyun ^{[1
,2
]}

Kim, Dae San ^{[3
]}

Kwon, Jongkyum ^{[4
,5
]}

Dolgy, Dmitry V. ^{[6
]}

机构：

[1] Tianjin Polytech Univ, Dept Math, Coll Sci, Tianjin 300160, Peoples R China

[2] Kwangwoon Univ, Dept Math, Seoul 139701, South Korea

[3] Sogang Univ, Dept Math, Seoul 121742, South Korea

[4] Gyeongsang Natl Univ, Dept Math Educ, Jinju 52828, Gyeongsangnamdo, South Korea

[5] Gyeongsang Natl Univ, ERI, Jinju 52828, Gyeongsangnamdo, South Korea

[6] Kwangwoon Univ, Seoul 139701, South Korea

来源：

MATHEMATICS | 2018年 / 6卷 / 10期

基金：

新加坡国家研究基金会;

关键词：

chebyshev polynomials of second kind; Fibonacci polynomials; sums of finite products; orthogonal polynomials;

D O I：

10.3390/math6100210

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper is concerned with representing sums of the finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials in terms of several classical orthogonal polynomials. Indeed, by explicit computations, each of them is expressed as linear combinations of Hermite, generalized Laguerre, Legendre, Gegenbauer and Jacobi polynomials, which involve the hypergeometric functions 1F1 and 2F1.

引用

页数：14

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