Preprint Short Note Version 1 This version is not peer-reviewed

A Determinantal Expression and a Recurrence Relation for the Euler Polynomials

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

Comments (3)

Comment 1
Received: 26 March 2017
Commenter: kader
The commenter has declared there is no conflict of interests.
Comment: bel article
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Comment 2
Received: 13 August 2017
Commenter: Feng Qi
Commenter's Conflict of Interests: I am the corresponding author of this paper.
Comment: This preprint has been formally accepted by Advances and Applications in Mathematical Sciences for publication in 2017.
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Comment 3
Received: 20 September 2017
Commenter: Feng Qi
Commenter's Conflict of Interests: I am the first and corresponding author for this preprint
Comment: This preprint has been formally published as

Feng Qi and Bai-Ni Guo, A determinantal expression and a recurrence relation for the Euler polynomials, Advances and Applications in Mathematical Sciences 16 (2017), no. 9, 297--309.
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