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Simplification of Coefficients in Differential Equations Associated with Higher Order Frobenius–Euler Numbers
: Received: 4 August 2017 / Approved: 4 August 2017 / Online: 4 August 2017 (15:47:44 CEST)
In the paper, by virtue of the Fa`a di Bruno formula, some properties of the Bell polynomials of the second kind, and the inversion formulas of binomial numbers and the Stirling numbers of the first and second kinds, the authors simplify meaningfully and significantly coefficients in two families of ordinary differential equations associated with higher order Frobenius–Euler numbers.
simplification; coefficient; ordinary differential equation; higher order Frobenius–Euler number; Fa`a di Bruno formula; Bell polynomial of the second kind; inversion formula
Computer Science and Mathematics, Analysis
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