Abstract
The usual developments of Newton's identities, the relation between the elementary symmetric functions of xl, x2, .. ., xn and the sums of the powers of the xi, are unsatisfactory, for they all involve a trick of one kind or another. In this note we show that with the proper notation, the derivation of Newton's identities is both natural and simple. The elementary symmetric functions of xl, .. ., xn are Sk= E Xl x1x* x Xik for k = 1, 2, ... ,n, 1 <'I <i2 < . . 1 <ik <n and the Newton functions are:
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