Recurrence Relations for Values of the Riemann Zeta Function in Odd Integers
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It is commonly known that ζ(2(k - 1)) = q_k - 1ζ(2k)/π^2 with known rational numbers q_k - 1. In this work we construct recurrence relations of the form ∑_k = 1^∞r_kζ(2k + 1)/π^2k = 0 and show that series representations for the coefficients r_k∈R can be computed explicitly.
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