REMARKABLE RELATIONS BETWEEN THE CENTRAL BINOMIAL SERIES, EULERIAN POLYNOMIALS, AND POLY-BERNOULLI NUMBERS, LEADING TO STEPHAN'S OBSERVATION
2023 年 77 巻 1 号 p. 149-158
詳細
2023 年 77 巻 1 号 p. 149-158
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.
