Hypergeometric Euler numbers
Number Theory
2021-03-01 v2
Abstract
In this paper, we introduce the hypergeometric Euler number as an analogue of the hypergeometric Bernoulli number and the hypergeometric Cauchy number. We study several expressions and sums of products of hypergeometric Euler numbers. We also introduce complementary hypergeometric Euler numbers and give some characteristic properties. There are strong reasons why these hypergeometric numbers are important. The hypergeometric numbers have one of the advantages that yield the natural extensions of determinant expressions of the numbers, though many kinds of generalizations of the Euler numbers have been considered by many authors.
Cite
@article{arxiv.1612.06210,
title = {Hypergeometric Euler numbers},
author = {Takao Komatsu and Huilin Zhu},
journal= {arXiv preprint arXiv:1612.06210},
year = {2021}
}