Fourier series of functions involving higher-order ordered Bell polynomials

Kim, Taekyun; Ким, Дае Сан; Jang, Gwan-Woo; Jang, Lee-Chae

doi:10.1515/math-2017-0134

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2018

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“…The Chebyshev polynomials belong to the family of orthogonal polynomials. We let the interested reader refer to [1][2][3][4] for more details on these.…”

Section: Introductionmentioning

confidence: 99%

Representation by Chebyshev Polynomials for Sums of Finite Products of Chebyshev Polynomials

et al. 2018

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In this paper, we consider sums of finite products of Chebyshev polynomials of the first, third, and fourth kinds, which are different from the previously-studied ones. We represent each of them as linear combinations of Chebyshev polynomials of all kinds whose coefficients involve some terminating hypergeometric functions 2 F 1 . The results may be viewed as a generalization of the linearization problem, which is concerned with determining the coefficients in the expansion of the product of two polynomials in terms of any given sequence of polynomials. These representations are obtained by explicit computations.

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“…The Chebyshev polynomials belong to the family of orthogonal polynomials. We let the interested reader refer to [1][2][3][4] for more details on these.…”

Section: Introductionmentioning

confidence: 99%

Representation by Chebyshev Polynomials for Sums of Finite Products of Chebyshev Polynomials

et al. 2018

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show abstract

“…We know that Bernoulli, Euler and Genocchi numbers and polynomials appear everywhere in mathematics (for example, see [1,6,[14][15][16]18,[21][22][23]). The Bernoulli, Euler and Genocchi numbers have been defined by the generating functions t e t −1 = m≥0 B m…”

Section: Introductionmentioning

confidence: 99%