Novel identities for elementary and complete symmetric polynomials with diverse applications
Copyright policy )Novel identities for elementary and complete symmetric polynomials with diverse applications
<p>This article aims to present novel identities for elementary and complete symmetric polynomials and explore their applications, particularly to generalized Vandermonde and special tri-diagonal matrices. It also extends existing results on Jacobi polynomials $ P_n^{(\alpha, \beta)}(x) $ and introduces an explicit formula based on the zeros of $ P_{n-1}^{(\alpha, \beta)}(x) $. Several illustrative examples are included.</p>
tri-diagonal matrix, jacobi polynomials, schur convexity, elementary symmetric polynomials, QA1-939, complete symmetric polynomials, vandermonde matrix, Mathematics
tri-diagonal matrix, jacobi polynomials, schur convexity, elementary symmetric polynomials, QA1-939, complete symmetric polynomials, vandermonde matrix, Mathematics
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