Nonlinear differential equations arising from Boole numbers and their applications
Taekyun Kim, Dae San Kim
TL;DR
This paper investigates nonlinear differential equations related to the generating function of Boole numbers, deriving new identities and exploring their applications in mathematical analysis.
Contribution
It introduces novel nonlinear differential equations for Boole numbers' generating functions and derives new identities involving higher-order Boole numbers.
Findings
Derived explicit identities involving Boole numbers.
Established nonlinear differential equations for generating functions.
Connected results to applications in mathematical analysis.
Abstract
In this paper, we study nonlinear differential equations satisfied by the generating function of Boole numbers. In addition, we derive some explicit and new interesting identities involving Boole numbers and higher-order numbers arising from our nonlinear differential equations.
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Taxonomy
TopicsNonlinear Waves and Solitons · Polynomial and algebraic computation · Mathematical and Theoretical Analysis