Preprint Short Note Version 1 NOT YET PEER-REVIEWED

A Determinantal Expression and a Recurrence Relation for the Euler Polynomials

Feng Qi 1,2,3,* and Bai-Ni Guo 4
1
Institute of Mathematics, Henan Polytechnic University, Jiaozuo 454010, Henan~Province, China
2
College of Mathematics, Inner Mongolia University for Nationalities, Tongliao 028043, Inner Mongolia Autonomous Region, China
3
Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin 300387, China
4
School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo~454010, Henan Province, China
Version 1 : Received: 11 October 2016 / Approved: 11 October 2016 / Online: 11 October 2016 (10:40:02 CEST)

How to cite: Qi, F.; Guo, B. A Determinantal Expression and a Recurrence Relation for the Euler Polynomials. Preprints 2016, 2016100034 (doi: 10.20944/preprints201610.0034.v1). Qi, F.; Guo, B. A Determinantal Expression and a Recurrence Relation for the Euler Polynomials. Preprints 2016, 2016100034 (doi: 10.20944/preprints201610.0034.v1).

Abstract

In the paper, by a very simple approach, the author establishes an expression in terms of a lower Hessenberg determinant for the Euler polynomials. By the determinantal expression, the author finds a recurrence relation for the Euler polynomials. By the way, the author derives the corresponding expression and recurrence relation for the Euler numbers.

Subject Areas

determinantal expression; recurrence relation; Euler polynomial; Euler number; Hessenberg determinant

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