Simplifying coefficients in differential equations associated with higher order Bernoulli numbers of the second kind

Feng Qi; Da-Wei Niu; Bai-Ni Guo

doi:10.3934/math.2019.2.170

AIMS Mathematics (Feb 2019)

Simplifying coefficients in differential equations associated with higher order Bernoulli numbers of the second kind

Feng Qi,
Da-Wei Niu,
Bai-Ni Guo

Affiliations

Feng Qi: 1 School of Mathematical Sciences, Tianjin Polytechnic University, Tianjin 300387, China 2 College of Mathematics, Inner Mongolia University for Nationalities, Tongliao 028043, China 4 School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo 454010, China
Da-Wei Niu: 3 Department of Mathematics, East China Normal University, Shanghai 200241, China
Bai-Ni Guo: 4 School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo 454010, China

DOI: https://doi.org/10.3934/math.2019.2.170
Journal volume & issue: Vol. 4, no. 2
pp. 170 – 175

Abstract

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In the paper, by virtue of the Faà di Bruno formula, some properties of the Bell polynomials of the second kind, and an inversion formula for the Stirling numbers of the first and second kinds, the authors establish meaningfully and significantly two identities which simplify coefficients in a family of ordinary differential equations associated with higher order Bernoulli numbers of the second kind.

Published in AIMS Mathematics

ISSN: 2473-6988 (Online)
Publisher: AIMS Press
Country of publisher: United States
LCC subjects: Science: Mathematics
Website: http://www.aimspress.com/journal/Math

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