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Jan
16
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?
Jan
12
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.
Jan
12
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.
Jan
12
comment What is $0^{i}$?
@hjhjhj57 I mention that the mean of this diverging series is $0$.
Jan
12
comment What is $0^{i}$?
@hjhjhj57 why u do not criticize Slade for the same?
Jan
12
comment What is $0^{i}$?
No, it is not wrong, it is widely accepted defginition. Prove it is wrong.
Jan
12
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.
Jan
12
comment What is $0^{i}$?
@soultrane i-th order derivative of sine is $i \sinh (\frac \pi 2-ix)$: tinyurl.com/kdmdkvf
Jan
12
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).
Jan
12
comment What is $0^{i}$?
@hjhjhj57 yes, and what?
Jan
12
comment What is $0^{i}$?
@hjhjhj57 $e^{-i \pi}=-1$, so $e^{-i \infty}=e^{-i \pi \infty}=(-1)^{-\infty}$. Also, $(-1)^x=\cos (\pi x) + i \sin (\pi x)$
Jan
12
comment What is $0^{i}$?
@hjhjhj57 what inequality?
Jan
12
comment What is $0^{i}$?
Why the downvote?
Jan
9
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 $\zeta(1)=-\gamma$.
Jan
9
comment Closed form for generating function of Riemann Xi function
@mike fixed, thanks (although I think using limit one can easily overcome the issue).
Jan
9
comment Closed form for generating function of Riemann Xi function
@mike it is Rieman Xi-function en.wikipedia.org/wiki/Riemann_Xi_function
Jan
8
comment Is $0$ a natural number?
That $\mathbb{N}$ usually includes zero. It is totally wrong.
Jan
8
comment Is $0$ a natural number?
This is wrong, -1
Jan
8
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.
Jan
7
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/…