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math.NT2024
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 n…
math.NT2024
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 t…