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December 2019 Several Properties of Multiple Hypergeometric Euler Numbers
Takao KOMATSU, Wenpeng ZHANG
Tokyo J. Math. 42(2): 551-570 (December 2019). DOI: 10.3836/tjm/1502179290

Abstract

In this paper, we introduce the higher order hypergeometric Euler numbers and show several interesting expressions. In 1875, Glaisher gave several interesting determinant expressions of numbers, including Bernoulli, Cauchy and Euler numbers. One advantage of hypergeometric numbers, including Bernoulli, Cauchy and Euler hypergeometric numbers, is the natural extension of determinant expressions of the numbers. As applications, we can get the inversion relations such that Euler numbers are elements in the determinant.

Citation

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Takao KOMATSU. Wenpeng ZHANG. "Several Properties of Multiple Hypergeometric Euler Numbers." Tokyo J. Math. 42 (2) 551 - 570, December 2019. https://doi.org/10.3836/tjm/1502179290

Information

Published: December 2019
First available in Project Euclid: 8 March 2019

zbMATH: 07209633
MathSciNet: MR4106592
Digital Object Identifier: 10.3836/tjm/1502179290

Subjects:
Primary: 11B68
Secondary: 11B37, 11C20, 15A15, 33C20

Rights: Copyright © 2019 Publication Committee for the Tokyo Journal of Mathematics

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Vol.42 • No. 2 • December 2019
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