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math.NT2021
Lerch's and the Polylogarithm at the Negative Integers
Jose Risomar Sousa
At the negative integers, there is a simple relation between the Lerch function and the polylogarithm. Starting from that relation and a formula for the polylogarithm at the ne…
math.CV2021
The Faulhaber Formula Analytic Continuation
Jose Risomar Sousa
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 expr…
math.NT2021
The Lerch Analytic Continuation
Jose Risomar Sousa
We demonstrate how to extend formulae for the Lerch transcendent function, , and the polylogarithm, , that only hold at the positive integers to…