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ON POLY-EULER NUMBERS

Part of: Sequences and sets

Published online by Cambridge University Press:  03 November 2016

YASUO OHNO  and
YOSHITAKA SASAKI
YASUO OHNO
Affiliation:
Mathematical Institute, Tohoku University, Sendai 980-8578, Japan email ohno@math.tohoku.ac.jp
YOSHITAKA SASAKI*
Affiliation:
Liberal Arts Education Center, Osaka University of Health and Sport Sciences, Asashirodai 1-1, Kumatori-cho, Sennan-gun, Osaka 590-0496, Japan email ysasaki@ouhs.ac.jp
*
✉ysasaki@ouhs.ac.jp
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Abstract

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Poly-Euler numbers are introduced as a generalization of the Euler numbers in a manner similar to the introduction of the poly-Bernoulli numbers. In this paper, some number-theoretic properties of poly-Euler numbers, for example, explicit formulas, a Clausen–von Staudt type formula, congruence relations and duality formulas, are given together with their combinatorial properties.

Keywords

Euler numberpoly-Euler numberpoly-Bernoulli numberClausen–von Staudt theorem

MSC classification

Primary: 11B68: Bernoulli and Euler numbers and polynomials
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 103 , Issue 1 , August 2017 , pp. 126 - 144
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

Footnotes

The first author was partly supported by Grant-in-Aid for Scientific Research (C) No. 23540036, 15K04774, and the second author was partly supported by Grant-in-Aid for Young Scientists (B) No. 23740036, 15K17524.

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