AIMS Mathematics, 2019, 4(2): 170-175. doi: 10.3934/math.2019.2.170

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

1 School of Mathematical Sciences, Tianjin Polytechnic University, Tianjin 300387, China
2 College of Mathematics, Inner Mongolia University for Nationalities, Tongliao 028043, China
3 Department of Mathematics, East China Normal University, Shanghai 200241, China
4 School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo 454010, China

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.
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