Famous Theorems of Mathematics/π is transcendental/Elementary symmetric polynomials

Let there be a polynomial of degree By the Fundamental Theorem of Algebra, it has complex roots (with multiplicity). Then we can write: As we know, Vieta's formulae link between the coefficients and roots of a polynomial: As we can see, these sums are symmetric polynomial, and are called elementary symmetric polynomials. Definition The elementary symmetric polynomials in variables , are defined as such: Elementary symmetric polynomials Symmetric polynomials Fundamental theorem of symmetric polynomials