Polylogarithms, Functional Equations and More: The Elusive Essays of William Spence (1777--1815) (2013)
The little-known Scottish mathematician William Spence was an able analyst, one of the first in Britain to be conversant with recent continental advances, and having original views. His major work on logarithmic transcendents gives the first detailed account of polylogarithms and related functions. A theory of algebraic equations was published just after his early death; and further essays, edited by John Herschel, were published posthumously. The most substantial of these concern an extension of his work on logarithmic transcendents, and the general solution of linear differential and difference equations. But awareness of Spence's works was long delayed by their supposed unavailability. Spence's life, the story of his lost publications, and a summary of all his essays are here described.
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