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Math Help - power sums + find formula for arbitrary n

  1. #1
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    power sums + find formula for arbitrary n

    Consider the power sums p1= x1 + ... + xn, p2= x1^2 + ... + xn^2,..., x1^n +...+ xn^n. These are polynomials in the elementary symmetric functions which Artin denotes by a1,...,an they must therefore be expressible as polynomials in a1,...,an. do this explicitly for n=4. Can you find the formula for arbitrary n?
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  2. #2
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    Quote Originally Posted by dabien View Post
    Consider the power sums p1= x1 + ... + xn, p2= x1^2 + ... + xn^2,..., x1^n +...+ xn^n. These are polynomials in the elementary symmetric functions which Artin denotes by a1,...,an they must therefore be expressible as polynomials in a1,...,an. do this explicitly for n=4. Can you find the formula for arbitrary n?
    see Newton's identity.
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