Colloquium Announcement
Department of Mathematics
West Virginia University


Thursday, February 26, 1998, at 3:45pm in 324 Armstrong Hall

(Tea and cookies begin at 3:00 in coffee room.)

Professor Henry W. Gould


The Girard-Waring Power Sum Formulas for Symmetric Functions

The talk will be suitable for a general audience.

Students are strongly encouraged to participate.


Albert Girard published formulas in Amsterdam in 1629 and Edward Waring published similar material in Cambridge in 1762-1782 that may be derived from the earlier work of Isaac Newton. These formulas concern expansions of functions of roots of polynomials by use of symmetric functions of the roots of the polynomials. Special cases for the sums of powers of roots turn up frequently in the literature without any indication of the antiquity of these ideas. We offer here some remarks on the basic Girard-Waring expansions and illustrate useful expansions arising from them. Over the years some mathematicians have tried to use such expansions to prove Fermat's (sic) Last Theorem. Many curious identities for things like Fibonacci numbers come from these formulas.
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