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arXiv · 2107.04972

The Faulhaber Formula Analytic Continuation

Jose Risomar Sousa
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Abstract

We extend the Faulhaber formula to the whole complex plane, obtaining an expression that fully resembles the Euler-Maclaurin summation formula, only it's exact. Thereafter, an expression for the generalized harmonic progressions valid in the whole complex plane is also derived. Lastly, we extend a formula for the Hurwitz zeta function valid at the negative integers, $\zeta(-k,b)$, to the whole complex plane, following a similar procedure.

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Jose Risomar Sousa. 2021-07-11. The Faulhaber Formula Analytic Continuation. https://arxiv.org/abs/2107.04972

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