REMARKABLE RELATIONS BETWEEN THE CENTRAL BINOMIAL SERIES, EULERIAN POLYNOMIALS, AND POLY-BERNOULLI NUMBERS, LEADING TO STEPHAN'S OBSERVATION

IF 0.6 4区数学 Q3 MATHEMATICS

Kyushu Journal of Mathematics Pub Date : 2023-01-01 DOI:10.2206/kyushujm.77.149

Beáta BÉNYI, Toshiki MATSUSAKA

引用次数: 0

Abstract

The central binomial series at negative integers are expressed as a linear combination of values of certain two polynomials. We show that one of the polynomials is a special value of the bivariate Eulerian polynomial and the other polynomial is related to the anti-diagonal sum of poly-Bernoulli numbers. As an application, we prove Stephan's observation from 2004.

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中心二项式级数、欧拉多项式和多伯努利数之间的显著关系，导致了斯蒂芬的观察

中心二项式级数在负整数处被表示为两个多项式值的线性组合。我们证明了其中一个多项式是二元欧拉多项式的一个特殊值，另一个多项式与多元伯努利数的反对角和有关。作为应用，我们证明了Stephan从2004年开始的观察。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Kyushu Journal of Mathematics 数学-数学

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Kyushu Journal of Mathematics is an academic journal in mathematics, published by the Faculty of Mathematics at Kyushu University since 1941. It publishes selected research papers in pure and applied mathematics. One volume, published each year, consists of two issues, approximately 20 articles and 400 pages in total. More than 500 copies of the journal are distributed through exchange contracts between mathematical journals, and available at many universities, institutes and libraries around the world. The on-line version of the journal is published at "Jstage" (an aggregator for e-journals), where all the articles published by the journal since 1995 are accessible freely through the Internet.