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Komatsu, Takao; Zhu, Huilin

Hypergeometric Euler numbers. (English) Zbl 1484.11077

AIMS Math. 5, No. 2, 1284-1303 (2020).
Summary: 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.

Cited in 9 Documents

MSC:

11B68 Bernoulli and Euler numbers and polynomials
11C20 Matrices, determinants in number theory
33C20 Generalized hypergeometric series, \({}_pF_q\)

Keywords:

hypergeometric Euler numbers; Euler numbers; Bernoulli numbers; Hasse-Teichmuller derivative; sums of products; determinants

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References:

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