Studies in Sums of Finite Products of the Second, Third, and Fourth Kind Chebyshev Polynomials

Taekyun Kim, Dae San Kim, Hyunseok Lee and Jongkyum Kwon
Additional contact information
Taekyun Kim: School of Science, Xi’an Technological University, Xi’an 710021, China
Dae San Kim: Department of Mathematics, Sogang University, Seoul 121-742, Korea
Hyunseok Lee: Department of Mathematics, Kwangwoon University, Seoul 139-701, Korea
Jongkyum Kwon: Department of Mathematics Education and ERI, Gyeongsang National University, Jinju 52828, Korea

Mathematics, 2020, vol. 8, issue 2, 1-17

Abstract: In this paper, we consider three sums of finite products of Chebyshev polynomials of two different kinds, namely sums of finite products of the second and third kind Chebyshev polynomials, those of the second and fourth kind Chebyshev polynomials, and those of the third and fourth kind Chebyshev polynomials. As a generalization of the classical linearization problem, we represent each of such sums of finite products as linear combinations of Hermite, generalized Laguerre, Legendre, Gegenbauer, and Jacobi polynomials. These are done by explicit computations and the coefficients involve terminating hypergeometric functions 2 F 1 , 1 F 1 , 2 F 2 , and 4 F 3 .

Keywords: sums of finite products; Chebyshev polynomials of the second; third and fourth kinds; terminating hypergeometric functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/2/210/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/2/210/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:8:y:2020:i:2:p:210-:d:317611

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().