Sums of finite products of Chebyshev polynomials of two different types

被引：3

作者：

Kim, Taekyun ^{[1
]}

Kim, Dae San ^{[2
]}

Dolgy, Dmitry, V ^{[3
]}

Kwon, Jongkyum ^{[4
]}

机构：

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

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

[3] Kwangwoon Univ, Kwangwoon Glocal Educ Ctr, Seoul 139701, South Korea

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

来源：

AIMS MATHEMATICS | 2021年 / 6卷 / 11期

关键词：

Chebyshev polynomials of the first; second; third and fourth kinds; terminating hypergeometric function; BERNOULLI; IDENTITIES;

D O I：

10.3934/math.2021722

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider sums of finite products of the second and third type Chebyshev polynomials, those of the second and fourth type Chebyshev polynomials and those of the third and fourth type Chebyshev polynomials, and represent each of them as linear combinations of Chebyshev polynomials of all types. Here the coefficients involve some terminating hypergeometric functions F-2(1). This problem can be viewed as a generalization of the classical linearization problems and is done by explicit computations.

引用

页码：12528 / 12542

页数：15

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