| Abstract: |
Several recent papers [1,2,3] have explored the work of Fa\'a di Bruno
(1855) and his near-contemporaries on the series expansion of
composite functions. Here, earlier work unnoticed in these papers is
described. These anticipate many of the results attributed to later
writers. This earlier work originates with Arbogast [4], with later
reworkings by Knight [5], West [6], De Morgan [7] and others.
1. Harley Flanders, From Ford to Fa\'a. Amer. Math. Monthly 108
(2001), 559-561.
2. Henry W. Gould, The Generalized Chain Rule of Differentiation
with Historical Notes. Utilitatis Mathematica 61 (2002), 97-106.
3. Warren P. Johnson, The Curious History of Fa\'a di Bruno's Formula.
Amer. Math. Monthly 109 (2002), 217-234.
4. Louis Francois Antoine Arbogast, Du Calcul des Derivations,
Strasbourg: Levrault, 1800.
5. Thomas Knight, On the Expansion of any Functions of Multinomials.
Philos. Trans. R. Soc. London, (1811: Pt.1), 49-88.
6. John West, Mathematical Treatises... edited ... by the late Sir
John Leslie ... accompanied by a memoir of ... the author by Edward
Sang. Edinburgh: Oliver & Boyd, London: Simpkin, Marshall & Co., 1838.
7. Augustus De Morgan, On Arbogast's Formulae of Expansion.
Cambridge and Dublin Math. J., 1 (1846) ( Camb. Math. J. 5),
238-255.
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