Preprint Article Version 1 This version not peer reviewed

Simplifying Coefficients in Differential Equations Associated with Higher Order Bernoulli Numbers of the Second Kind

Version 1 : Received: 5 August 2017 / Approved: 8 August 2017 / Online: 8 August 2017 (07:59:57 CEST)

How to cite: Qi, F.; Niu, D.; Guo, B. Simplifying Coefficients in Differential Equations Associated with Higher Order Bernoulli Numbers of the Second Kind. Preprints 2017, 2017080026 (doi: 10.20944/preprints201708.0026.v1). Qi, F.; Niu, D.; Guo, B. Simplifying Coefficients in Differential Equations Associated with Higher Order Bernoulli Numbers of the Second Kind. Preprints 2017, 2017080026 (doi: 10.20944/preprints201708.0026.v1).

Abstract

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.

Subject Areas

simplification; coefficient; ordinary differential equation; higher order Bernoulli number of the second kind; Stirling number of the first kind; Stirling number of the second kind; inversion formula; Bell polynomial of the second kind; Faà di Bruno formula.

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