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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