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Meditations on the product rule. (English) Zbl 0581.05007

The author considers n arbitrary (adequately differentiable) functions of a variable x, the derivatives of various orders of them and their products, and the algebraic relations that hold between these quantities. The product-rule of differentiation is a simple example of such a relation. A more complicated one was used by the author to enumerate rooted Eulerian and bicubic planar maps. The author discusses the latter formula and relates one subcase to the power series in Lagrange’s Theorem.

MSC:

05A15 Exact enumeration problems, generating functions
05A10 Factorials, binomial coefficients, combinatorial functions
40A05 Convergence and divergence of series and sequences
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References:

[1] Good, I. J.,Generalizations to several variables of Lagrange’s expansion, with applications to stochastic processes. Proc. Cambridge Philos. Soc.56 (1960), 367–380. · Zbl 0135.18802
[2] Tutte, W. T.,A census of slicings. Canad. J. Math.14 (1962), 708–722. · Zbl 0111.35202
[3] Tutte, W. T.,On elementary calculus and the Good formula. J. Combin. Theory Ser. B18 (1975), 97–137. · Zbl 0307.05003
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