Waring's expression for a symmetric function in terms of sums of like powers
- 1 February 1909
- journal article
- research article
- Published by Cambridge University Press (CUP) in Proceedings of the Edinburgh Mathematical Society
- Vol. 27, 5-9
- https://doi.org/10.1017/s001309150000211x
Abstract
1. In his Miscellanea Analytica of the year 1762, Waring stated the identitieswhere sp stands for the sum of the pth powers of n quantities α, β, γ,…. If the identities be written in the uncontracted formit is readily seen that they hold not merely for certain powers of certain quantities, but for any quantities whatever; and that, indeed, for the elements of the arraywe may legitimately substitute in order the elements of the arraythus obtaining the identitiesThese latter were given by Binet in 1812, and are usually, but with little real justification, spoken of as “Binet's Identities.”Keywords
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