Dolgy, D.V.; Kim, D.S.; Kim, T.; Kwon, J. Connection Problem for Sums of Finite Products of Chebyshev Polynomials of the Third and Fourth Kinds. Symmetry2018, 10, 617.
Dolgy, D.V.; Kim, D.S.; Kim, T.; Kwon, J. Connection Problem for Sums of Finite Products of Chebyshev Polynomials of the Third and Fourth Kinds. Symmetry 2018, 10, 617.
Dolgy, D.V.; Kim, D.S.; Kim, T.; Kwon, J. Connection Problem for Sums of Finite Products of Chebyshev Polynomials of the Third and Fourth Kinds. Symmetry2018, 10, 617.
Dolgy, D.V.; Kim, D.S.; Kim, T.; Kwon, J. Connection Problem for Sums of Finite Products of Chebyshev Polynomials of the Third and Fourth Kinds. Symmetry 2018, 10, 617.
Abstract
This paper treats the connection problem of expressing sums of finite products of Chebyshev polynomials of the third and fourth kinds in terms of five classical orthogonal polynomials. In fact, by carrying out explicit computations each of them are expressed as linear combinations of Hermite, generalized Laguerre, Legendre, Gegenbauer, and Jacobi polynomials which involve some terminating hypergeometric functions ${}_2 F_0, {}_2 F_1$, and ${}_3 F_2$.
Keywords
sums of finite products of chebyshev polynomials of the third and fourth kinds; Hermite; generalized Laguerre; Legendre; Gegenbauer; Jacobi
Subject
Computer Science and Mathematics, Analysis
Copyright:
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