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In mathematics, Borel summation is a summation method for divergent series, It is particularly useful for summing divergent asymptotic series, and in some sense gives the best possible sum for such series , I want to know if it is possible to apply the one of methods of Borel summation for Riemann zeta function .then my question here is :

Question: Could be Borel summation applied for Riemann zeta function in the strip region ?

zeraoulia rafik
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  • Try applying to $a_k(s) = (-1)^{k+1}k^{-s}$ the same method as there. It should converge to $\eta(s) = (1-2^{1-s}) \zeta(s)$ at least with the Borel's integral summation method with analytic continuation – reuns Mar 17 '17 at 18:14

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