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 Jan16 comment Why we cannot ascribe values to behavior of functions at poles? Well. What do u think will happen if we postulate $a \omega =\omega$ but $\omega+a\ne \omega$, $\omega-\omega$ undefined? Jan12 comment What is $0^{i}$? @soultrane there are multiple formulas, all give the same result, why you do not like it? I can explain with details. Wolfram specifics are not involved. Jan12 comment What is $0^{i}$? @soultrane the number after "^" determines the derivative order. Win $0$ it gives sin, with $1$ it gives cosine, with -1 it gives -cosine etc. But it is off-topic here, I can explain with more details as a separate answer to your question. Jan12 comment What is $0^{i}$? @hjhjhj57 I mention that the mean of this diverging series is $0$. Jan12 comment What is $0^{i}$? @hjhjhj57 why u do not criticize Slade for the same? Jan12 comment What is $0^{i}$? No, it is not wrong, it is widely accepted defginition. Prove it is wrong. Jan12 comment What is $0^{i}$? "follows the convention $0^x=0$" - where u got this "convention" from? "and $0^0=0$ is questionable" - it is not questionable, it it plainly wrong, it is usually define to be 1 or left undefined. Jan12 comment What is $0^{i}$? @soultrane i-th order derivative of sine is $i \sinh (\frac \pi 2-ix)$: tinyurl.com/kdmdkvf Jan12 comment What is $0^{i}$? @hjhjhj57 the topic starter already indicated that the limit does not exist, so this comment does not add anything. He was asking what value can be assigned to it nevertheless. The mean value of the sequence is $0$ (see my ansswer). Jan12 comment What is $0^{i}$? @hjhjhj57 yes, and what? Jan12 comment What is $0^{i}$? @hjhjhj57 $e^{-i \pi}=-1$, so $e^{-i \infty}=e^{-i \pi \infty}=(-1)^{-\infty}$. Also, $(-1)^x=\cos (\pi x) + i \sin (\pi x)$ Jan12 comment What is $0^{i}$? @hjhjhj57 what inequality? Jan12 comment What is $0^{i}$? Why the downvote? Jan9 comment Closed form for generating function of Riemann Xi function @Nicholas Pipitone okay, this all is not important. One can take $\Gamma(0)=\gamma$ and $\zeta(1)=-\gamma$. Jan9 comment Closed form for generating function of Riemann Xi function @mike fixed, thanks (although I think using limit one can easily overcome the issue). Jan9 comment Closed form for generating function of Riemann Xi function @mike it is Rieman Xi-function en.wikipedia.org/wiki/Riemann_Xi_function Jan8 comment Is $0$ a natural number? That $\mathbb{N}$ usually includes zero. It is totally wrong. Jan8 comment Is $0$ a natural number? This is wrong, -1 Jan8 comment Is $0$ a natural number? @Charles Stewart for me its totally opposite, natural numbers were always 1,2,3... and I have never heard about "whole numbers" before your comment. Jan7 comment Is split-complex $j=i+2\epsilon$? Good points but what is with the 2x2 matrices then? They should form a good ring I think. Also what do u think about this question? math.stackexchange.com/questions/226850/…