Kim, T.; Kim, D.S.; Kwon, J.; Dolgy, D.V. Expressing Sums of Finite Products of Chebyshev Polynomials of the Second Kind and of Fibonacci Polynomials by Several Orthogonal Polynomials. Mathematics2018, 6, 210.
Kim, T.; Kim, D.S.; Kwon, J.; Dolgy, D.V. Expressing Sums of Finite Products of Chebyshev Polynomials of the Second Kind and of Fibonacci Polynomials by Several Orthogonal Polynomials. Mathematics 2018, 6, 210.
Kim, T.; Kim, D.S.; Kwon, J.; Dolgy, D.V. Expressing Sums of Finite Products of Chebyshev Polynomials of the Second Kind and of Fibonacci Polynomials by Several Orthogonal Polynomials. Mathematics2018, 6, 210.
Kim, T.; Kim, D.S.; Kwon, J.; Dolgy, D.V. Expressing Sums of Finite Products of Chebyshev Polynomials of the Second Kind and of Fibonacci Polynomials by Several Orthogonal Polynomials. Mathematics 2018, 6, 210.
Abstract
This paper is concerned with representing sums of 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 ${}_1 F_1$ and ${}_2 F_1$.
Keywords
Chebyshev polynomials of second kind; Fibonacci polynomials; sums of finite products; orthogonal polynomials
Subject
Computer Science and Mathematics, Analysis
Copyright:
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