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AIMS Mathematics

2020, Volume 5, Issue 2: 1284-1303. doi: 10.3934/math.2020088
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Research article

Hypergeometric Euler numbers

  • 1.
    Department of Mathematical Sciences, School of Science, Zhejiang Sci-Tech University, Hangzhou 310018, China
  • 2.
    School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
  • Received: 04 October 2019 Accepted: 10 December 2019 Published: 19 January 2020

  • MSC : 11B68, 11B37, 11C20, 15A15, 33C20

  • 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.

    Citation: Takao Komatsu, Huilin Zhu. Hypergeometric Euler numbers[J]. AIMS Mathematics, 2020, 5(2): 1284-1303. doi: 10.3934/math.2020088

    Related Papers:

  • 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.


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