多个超几何欧拉数的几个性质

Pub Date : 2019-12-01 DOI:10.3836/TJM/1502179290
T. Komatsu, Wenpeng Zhang
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引用次数: 3

摘要

本文引入了高阶超几何欧拉数,并给出了几个有趣的表达式。1875年,格莱舍给出了数的几个有趣的行列式,包括伯努利数、柯西数和欧拉数。包括伯努利、柯西和欧拉超几何数在内的超几何数的一个优点是它们的行列式的自然扩展。作为应用,我们可以得到欧拉数是行列式元素的逆关系。
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Several Properties of Multiple Hypergeometric Euler Numbers
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.
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