Prehistory of Faà di Bruno's Formula

  title={Prehistory of Fa{\`a} di Bruno's Formula},
  author={Alex D. D. Craik},
  journal={The American Mathematical Monthly},
  pages={119 - 130}
  • A. Craik
  • Published 1 February 2005
  • History
  • The American Mathematical Monthly
poraries on the series expansion of composite functions. Here, earlier work unnoticed in these papers is described. These anticipate many of the results attributed to others. This earlier work originates with Arbogast, with later reworkings by Knight, West, De Morgan, and others. The series expansion in powers of x of a suitably-differentiable composite function g(f(x)) has the form 
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A restatement in terms of set partitions can be proved easily in a few lines, as the authors shall see in Section 2, though it still requires a bit of work to pass from that form to the form in (1.1).
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  • T. Knight
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    Philosophical Transactions of the Royal Society of London
  • 1811
1. The expansion of multinomial functions has, of late, been so ably and fully treated by M. Arbogast, in his learned work ‘Du Calcul des Dérivations,' that it may appear, perhaps, scarcely necessary
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Tis about two Years Since, that considering Mr. Newton's Theorem for Raising a Binomial to any given Power, or Extracting any Root of the Same; I enquired, whether What he had done for a Binomial,
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