Representation by several orthogonal polynomials for sums of finite products of Chebyshev polynomials of the first, third and fourth kinds

The classical linearization problem concerns with determining the coefficients in the expansion of the product of two polynomials in terms of any given sequence of polynomials. As a generalization of this, we consider here sums of finite products of Chebyshev polynomials of the first, third, and fou...

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Bibliographic Details
Published in:Advances in difference equations 2019-03, Vol.2019 (1), p.1-16, Article 110
Main Authors: Kim, Taekyun, Kim, Dae San, Dolgy, Dmitry V., Kim, Dojin
Format: Article
Language:English
Subjects:
Analysis
Chebyshev approximation
Chebyshev polynomials
Difference and Functional Equations
Extended Laguerre polynomial
Functional Analysis
Gegenbauer polynomial
Hermite polynomial
Hypergeometric functions
Legendre polynomial
Linearization
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Polynomials
Representations
Sums
Sums of finite products
Thermal expansion
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Summary:The classical linearization problem concerns with determining the coefficients in the expansion of the product of two polynomials in terms of any given sequence of polynomials. As a generalization of this, we consider here sums of finite products of Chebyshev polynomials of the first, third, and fourth kinds, which are different from the ones previously studied. We represent each of them as linear combinations of Hermite, extended Laguerre, Legendre, Gegenbauer, and Jacobi polynomials. Here, the coefficients involve some terminating hypergeometric functions F 1 2 , F 2 2 , and F 1 1 . These representations are obtained by explicit computations.
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-019-2058-8