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Open AccessArticle

Representing by Orthogonal Polynomials for Sums of Finite Products of Fubini Polynomials

1
Department of Mathematics, Sogang University, Seoul 04107, Korea
2
Kwangwoon Institute for Advanced Studies, Kwangwoon University, Seoul 01897, Korea
3
Department of Mathematics, Pusan National University, Busan 46241, Korea
4
Department of Mathematics, Kwangwoon University, Seoul 01897, Korea
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(4), 319; https://doi.org/10.3390/math7040319
Received: 12 March 2019 / Revised: 25 March 2019 / Accepted: 27 March 2019 / Published: 29 March 2019
(This article belongs to the Special Issue Special Polynomials)
In the classical connection problem, it is dealt with determining the coefficients in the expansion of the product of two polynomials with regard to any given sequence of polynomials. As a generalization of this problem, we will consider sums of finite products of Fubini polynomials and represent these in terms of orthogonal polynomials. Here, the involved orthogonal polynomials are Chebyshev polynomials of the first, second, third and fourth kinds, and Hermite, extended Laguerre, Legendre, Gegenbauer, and Jabcobi polynomials. These representations are obtained by explicit computations. View Full-Text
Keywords: fubini polynomials; orthogonal polynomials; Chebyshev polynomials; Hermite polynomials; extended laguerre polynomials; Legendre polynomials; Gegenbauer polynomials; Jabcobi polynomials fubini polynomials; orthogonal polynomials; Chebyshev polynomials; Hermite polynomials; extended laguerre polynomials; Legendre polynomials; Gegenbauer polynomials; Jabcobi polynomials
MDPI and ACS Style

Kim, D.S.; Dolgy, D.V.; Kim, D.; Kim, T. Representing by Orthogonal Polynomials for Sums of Finite Products of Fubini Polynomials. Mathematics 2019, 7, 319.

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