Simplifying coefficients in a family of nonlinear ordinary differential equations. (English) Zbl 1437.11038
Summary: By virtue of the Faá di Bruno formula, properties of the Stirling numbers and the Bell polynomials of the second kind, the binomial inversion formula, and other techniques in combinatorial analysis, the author finds a simple, meaningful, and signicant expression for coefficients in a family of nonlinear ordinary differential equations.
MSC:
| 11B73 | Bell and Stirling numbers |
| 11B83 | Special sequences and polynomials |
| 34A05 | Explicit solutions, first integrals of ordinary differential equations |
Keywords:
simplifying; coefficient; nonlinear ordinary differential equation; Faá di Bruno formula; Stirling number; Bell polynomials of the second kind; binomial inversion formula; Lah numberReferences:
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