Application of a composition of generating functions for obtaining explicit formulas of polynomials

Abstract

Using notions of composita and composition of generating functions, we obtain explicit formulas for the Chebyshev polynomials, the Legendre polynomials, the Gegenbauer polynomials, the Associated Laguerre polynomials, the Stirling polynomials, the Abel polynomials, the Bernoulli Polynomials of the Second Kind, the Generalized Bernoulli polynomials, the Euler Polynomials, the Peters polynomials, and the Narumi polynomials.

Original language	English
Pages (from-to)	161-171
Number of pages	11
Journal	Journal of Mathematical Analysis and Applications
Volume	404
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2013.03.009
Publication status	Published - 1 Aug 2013

Keywords

Composita
Composition of generating function
Generating function
Polynomial

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2013.03.009

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title = "Application of a composition of generating functions for obtaining explicit formulas of polynomials",

abstract = "Using notions of composita and composition of generating functions, we obtain explicit formulas for the Chebyshev polynomials, the Legendre polynomials, the Gegenbauer polynomials, the Associated Laguerre polynomials, the Stirling polynomials, the Abel polynomials, the Bernoulli Polynomials of the Second Kind, the Generalized Bernoulli polynomials, the Euler Polynomials, the Peters polynomials, and the Narumi polynomials.",

keywords = "Composita, Composition of generating function, Generating function, Polynomial",

author = "Kruchinin, {Dmitry V.} and Kruchinin, {Vladimir V.}",

year = "2013",

month = aug,

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doi = "10.1016/j.jmaa.2013.03.009",

language = "English",

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journal = "Journal of Mathematical Analysis and Applications",

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T1 - Application of a composition of generating functions for obtaining explicit formulas of polynomials

AU - Kruchinin, Dmitry V.

AU - Kruchinin, Vladimir V.

PY - 2013/8/1

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N2 - Using notions of composita and composition of generating functions, we obtain explicit formulas for the Chebyshev polynomials, the Legendre polynomials, the Gegenbauer polynomials, the Associated Laguerre polynomials, the Stirling polynomials, the Abel polynomials, the Bernoulli Polynomials of the Second Kind, the Generalized Bernoulli polynomials, the Euler Polynomials, the Peters polynomials, and the Narumi polynomials.

AB - Using notions of composita and composition of generating functions, we obtain explicit formulas for the Chebyshev polynomials, the Legendre polynomials, the Gegenbauer polynomials, the Associated Laguerre polynomials, the Stirling polynomials, the Abel polynomials, the Bernoulli Polynomials of the Second Kind, the Generalized Bernoulli polynomials, the Euler Polynomials, the Peters polynomials, and the Narumi polynomials.

KW - Composita

KW - Composition of generating function

KW - Generating function

KW - Polynomial

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JO - Journal of Mathematical Analysis and Applications

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