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∫ 1/2 0 E2m(x) csc(πx)dx ■ 5 Sums Of Negative Even Powers As previously noted, if we let S(s, n) = 2n−2 ∑ j=1 1 sins ( (2 j−1)π 2n ) 38 Then S(2, n) = 1 2 22n−2 S(4, n) = 1 6 ( 24n−4 + 2(22n−2) ) S(6, n) = 1 30 (2(26n−6) +5(24n−4) +8(22n−2) · 1916

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Sums of Powers of Sine and Generalized Bernoulli Polynomials

math.GM · 2025-02-21 · unverdicted · novelty 3.0

Formulas express specific sums of 1/sin^s at dyadic rational angles via generalized Bernoulli and Euler polynomials, yielding an integral form for zeta(s).

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Sums of Powers of Sine and Generalized Bernoulli Polynomials math.GM · 2025-02-21 · unverdicted · none · ref 2
Formulas express specific sums of 1/sin^s at dyadic rational angles via generalized Bernoulli and Euler polynomials, yielding an integral form for zeta(s).

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