The Faulhaber Formula Analytic Continuation
Complex Variables
2022-06-14 v3
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, , to the whole complex plane, following a similar procedure.
Cite
@article{arxiv.2107.04972,
title = {The Faulhaber Formula Analytic Continuation},
author = {Jose Risomar Sousa},
journal= {arXiv preprint arXiv:2107.04972},
year = {2022}
}
Comments
A typo was fixed, a better integral representation added. 5 pages