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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio


IMPACT FACTOR 2018: 0.551

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1572-9176
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Differential and integral equations for the 2-iterated Bernoulli, 2-iterated Euler and Bernoulli–Euler polynomials

Subuhi Khan / Mumtaz Riyasat
Published Online: 2018-11-21 | DOI: https://doi.org/10.1515/gmj-2018-0062

Abstract

The main goal of this article is to derive differential and associated integral equations for some 2-iterated and mixed type special polynomial families. By using the factorization method, the recurrence relations and differential equations are derived for the 2-iterated Bernoulli, 2-iterated Euler and Bernoulli–Euler polynomials. The Volterra integral equations for these polynomial families are also established. The graphical representation of these 2-iterated and mixed polynomials is presented. The zeros of these polynomials are investigated for certain values of the index n using numerical computation. The approximate solutions of the real zeros of these polynomials are also given.

Keywords: Bernoulli–Euler polynomials; differential equations; integral equations

MSC 2010: 33E20; 33E30

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About the article

Received: 2016-04-04

Accepted: 2017-09-06

Published Online: 2018-11-21


This work has been done under Post-Doctoral Fellowship (Office Memo No.2/40(38)/2016/RD-II/1063) awarded to Mumtaz Riyasat by the National Board of Higher Mathematics, Department of Atomic Energy, Government of India, Mumbai.


Citation Information: Georgian Mathematical Journal, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2018-0062.

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