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May
17
comment Concerning Hurwitz Zeta function, how to prove the following identity?
After I differentiate the expression under the integral I get something different. How do you get this?
May
17
comment Concerning Hurwitz Zeta function, how to prove the following identity?
Great! Is there a way to obtain a more general formula, that is with a variable instead of 0?
May
17
comment Concerning Hurwitz Zeta function, how to prove the following identity?
@tired I do not see how the formula is connected here.
May
7
comment Comparing infinite numbers
@Ben Crowell I always was wondering how one can reconcile diverging series with ordinals. I think I know a sketch.
May
7
comment Comparing infinite numbers
@Asaf Karagila see here: en.wikipedia.org/wiki/… Cardinality of $\omega$ is $\aleph_0$ se they are usually considered equal.
May
6
comment Comparing infinite numbers
@Asaf Karagila they do not. But the ordinal $\omega$ is usually identified with the cardinal $\aleph_0$ yet with different operations, see here: en.wikipedia.org/wiki/Ordinal_number .
May
6
comment Comparing infinite numbers
@Asaf Karagila exactly my point. The operations on surreals correspond not to the classical operations on ordinals but to the so-called "natural operations" (follow the second link).
May
6
comment Compare density of rationals to the density of integers
@Travis Can we compare the density of rationals to the density of a uniform dense countable set at all? For instance the density of rationals to the density of its subset - rationals with, say, even numerator or denomenator?
May
6
comment Compare density of rationals to the density of integers
OK, infinite but quantify it. Use ordinals, cardinals, complex numbers, whatever else. But in such a way that the desities came different.
May
6
comment Compare density of rationals to the density of integers
No, I want a measure where the desnsity of integers is not zero. And greater than the density of, say, evens.
Apr
25
comment What do you call the subset of all the Gaussian integers having the smallest magnitude given an argument?
No Wikipedia entry?
Apr
25
comment What do you call the subset of all the Gaussian integers having the smallest magnitude given an argument?
@mercio you are correct.
Apr
25
comment What do you call the subset of all the Gaussian integers having the smallest magnitude given an argument?
@Lee Mosher yes, typo
Apr
25
comment Is $\sum_{k=-\infty}^{0}f(-k)=\sum_{k=0}^{\infty} f(k)$ always?
@Alamos the first symbol definitely represents $\lim_{n\to\infty}\sum_{k=-n}^0f(k)$
Apr
25
comment Is $\sum_{k=-\infty}^{0}f(-k)=\sum_{k=0}^{\infty} f(k)$ always?
@Alamos divergent series depend on the order
Apr
25
comment Is $\sum_{k=-\infty}^{0}f(-k)=\sum_{k=0}^{\infty} f(k)$ always?
It this true for all summation techniques used for divergent series?
Apr
25
comment Is $\sum_{k=-\infty}^{0}f(-k)=\sum_{k=0}^{\infty} f(k)$ always?
I made a typo in the question, sorry.
Apr
4
comment Does it make sense to learn any other language except English, being a mathematician?
@Howard Langtone consider Gelfond, Calculus of finite differences (1959). inis.jinr.ru/sl/vol1/UH/_Ready/Mathematics/… It has been translated to English only in 1971 in India. It is the only book where I found criteria of possibility to represent an analytic function as Newton series.
Apr
1
comment Has anybody ever considered “full derivative”?
@columbus8myhw this is not closed form...
Apr
1
comment Has anybody ever considered “full derivative”?
@columbus8myhw it is not equal to e.