Korobov polynomials of the fifth kind and of the sixth kind

Dae San Kim; Taekyun Kim; Hyuck In Kwon; Toufik Mansour

doi:10.5666/KMJ.2016.56.2.329

Korobov polynomials of the fifth kind and of the sixth kind

Dae San Kim, Taekyun Kim, Hyuck In Kwon, Toufik Mansour

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Recently, Korobov polynomials have been received a lot of attention, which are discrete analogs of Bernoulli polynomials. In particular, these polynomials are used to derive some interpolation formulas of many variables and a discrete analog of the Euler summation formula. In this paper, we extend these family of polynomials to consider the Korobov polynomials of the fifth kind and of the sixth kind. We present several explicit formulas and recurrence relations for these polynomials. Also, we establish a connection between our polynomials and several known families of polynomials.

Original language	English
Pages (from-to)	329-342
Number of pages	14
Journal	Kyungpook Mathematical Journal
Volume	56
Issue number	2
DOIs	https://doi.org/10.5666/KMJ.2016.56.2.329
State	Published - 2016

Bibliographical note

Publisher Copyright:
© Kyungpook Mathematical Journal.

Keywords

Bernoulli polynomials
Frobenius-Euler polynomials
Korobov polynomials
Umbral calculus

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.5666/KMJ.2016.56.2.329

Cite this

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abstract = "Recently, Korobov polynomials have been received a lot of attention, which are discrete analogs of Bernoulli polynomials. In particular, these polynomials are used to derive some interpolation formulas of many variables and a discrete analog of the Euler summation formula. In this paper, we extend these family of polynomials to consider the Korobov polynomials of the fifth kind and of the sixth kind. We present several explicit formulas and recurrence relations for these polynomials. Also, we establish a connection between our polynomials and several known families of polynomials.",

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author = "Kim, {Dae San} and Taekyun Kim and Kwon, {Hyuck In} and Toufik Mansour",

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AU - Kim, Taekyun

AU - Kwon, Hyuck In

AU - Mansour, Toufik

N1 - Publisher Copyright: © Kyungpook Mathematical Journal.

PY - 2016

Y1 - 2016

N2 - Recently, Korobov polynomials have been received a lot of attention, which are discrete analogs of Bernoulli polynomials. In particular, these polynomials are used to derive some interpolation formulas of many variables and a discrete analog of the Euler summation formula. In this paper, we extend these family of polynomials to consider the Korobov polynomials of the fifth kind and of the sixth kind. We present several explicit formulas and recurrence relations for these polynomials. Also, we establish a connection between our polynomials and several known families of polynomials.

AB - Recently, Korobov polynomials have been received a lot of attention, which are discrete analogs of Bernoulli polynomials. In particular, these polynomials are used to derive some interpolation formulas of many variables and a discrete analog of the Euler summation formula. In this paper, we extend these family of polynomials to consider the Korobov polynomials of the fifth kind and of the sixth kind. We present several explicit formulas and recurrence relations for these polynomials. Also, we establish a connection between our polynomials and several known families of polynomials.

KW - Bernoulli polynomials

KW - Frobenius-Euler polynomials

KW - Korobov polynomials

KW - Umbral calculus

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JO - Kyungpook Mathematical Journal

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ER -

Korobov polynomials of the fifth kind and of the sixth kind

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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