Korobov Polynomials of the Fifth Kind and of the Sixth Kind

- Journal title : Kyungpook mathematical journal
- Volume 56, Issue 2, 2016, pp.329-342
- Publisher : Department of Mathematics, Kyungpook National University
- DOI : 10.5666/KMJ.2016.56.2.329

Title & Authors

Korobov Polynomials of the Fifth Kind and of the Sixth Kind

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

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

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.

Keywords

Bernoulli polynomials;Frobenius-Euler polynomials;Korobov polynomials;Umbral calculus;

Language

English

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