Sums of Powers of Sine and Generalized Bernoulli Polynomials

2025/02/21 by Leon D. Fairbanks, Fairbanks, Leon D.
Mathematics · #11M06 #Advanced Mathematical Identities #FOS: Mathematics #General Mathematics (math.GM) #Mathematical Inequalities and Applications #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2502.15966

openalex publication_date 2025/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We produce formulas for ∑_j=1^2^n-2(1)/(sin^s(((2j-1)π)/(2ⁿ))) in terms of Generalized Bernoulli and Euler polynomials and use one of the formulas to produce a nice integral representation of the Riemann zeta function.

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