All questions with tag [math: analytic-continuation]


Analytic continuation of an integral involving the Mittag-Leffler function

I have actually uploaded this inquiry on MO, and also I really did not get a solution. We have the adhering to integral: $$I(s)=\int_{0}^{\infty} \frac{s}{2x}\left(E_{s/2}((\pi x)^{s/2})-1\right)\omega(x)dx -\lim_{z \to 1 }\zeta(z)$$ where $E_{\alpha}(z)$ is the Mittag - Leffler function, $\omega(x)=\dfrac{\theta(ix)-1}{2}$ , $\theta(x)...
2022-07-09 23:30:13

Easy explanation of analytic continuation

Today, as I was skimming my duplicate of Higher Algebra by Barnard and also Child, I found a theory which claimed, The collection $$ 1+\frac{1}{2^p} +\frac{1}{3^p}+...$$ deviates for $p\leq 1$ and also merges for $p>1$. Yet later on I figured out that the zeta function is specified for all intricate values apart from 1. Currently I r...
2022-06-07 21:17:18