Preprint Short Note Version 1 NOT YET PEER-REVIEWED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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