Jose Risomar Sousa
Published 2021-01-18Version 1
We provide alternative expressions for the Lerch $\Phi$ and the polylogarithm functions, $\Phi(e^m,k,b)$ and $\mathrm{Li}_{k}(e^{m})$, respectively, and for their partial sums, valid when $\Re{(k)}>0$. These expressions are obtained through analytic continuation of the formulae valid at the positive integers.
Comments: arXiv admin note: text overlap with arXiv:2012.08558
Zeros of partial sums of the Riemann zeta-function
Zeros of partial sums of $L$-functions
Analytic Continuation of some zeta functions
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