Work

Remarkable relations between the central binomial series, Eulerian polynomials, and poly-Bernoulli numbers

Year: 2022

Type: preprint

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 antidiagonal sum of poly-Bernoulli numbers. As an application, we prove Stephan's observation from 2004.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2207.00205

Authors: Bényi, Beáta, Matsusaka, Toshiki

Institutions: Ludovika University of Public Service, Nagoya University

Language: English

Topic: Advanced Mathematical Identities

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Japan Society for the Promotion of Science

Awards: A new look into various arithmetic and topological invariants through the eyes of modular knots, Number theory of real quadratic fields from the perspective of non-holomorphic modular forms

OpenAlex ID: W4283816041

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