21st Century COE Lectures

Alex D.D. Craik

    Date : November 20 (Thu), 2003, 11:00-12:00
    Place : Room 115, RIMS
    Lecturer: Alex D.D. Craik
    School of Mathematics & Statistics, University of St Andrews, St Andrews, Fife KY16 9SS, Scotland, UK
    Title : Prehistory of Fa\'a di Bruno's formula
    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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Last modified: December 5, 2003