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Jun
18
comment Example of a function that has fractional derivatives of order less than 1 but not 1
With s=1 it is differentiable?
Jun
5
comment Solutions of sixth order polynomial equations
In what form do u want the solution - series, special functions, limit or anything else? Some computer algebra systems already have root of a polynomial as a built-in function.
May
19
comment Why is $\lim_{(x,y)\to(0,0)}\frac yx \ne 0$?
It is discontinuous at (0,0).
May
19
comment Why is $\lim_{(x,y)\to(0,0)}\frac yx \ne 0$?
Depending on your definition of the limit with two variables, it can be 0.
May
18
comment Can the Riemann Zeta derivative be expressed in terms of Riemann Zeta?
The problem with your addition part is also that polygamma is not defined for non-integer indexes as well.
May
17
comment Concerning Hurwitz Zeta function, how to prove the following identity?
Done: math.stackexchange.com/questions/1287008/…
May
17
comment Concerning Hurwitz Zeta function, how to prove the following identity?
Can the F.3.6 integrals be represented in closed form?
May
17
comment Concerning Hurwitz Zeta function, how to prove the following identity?
I've got the following: $$\int_0^{\infty } \frac{1}{4} (\coth (\pi t)-1) \left(a^2+t^2\right)^{-\frac{s}{2}} \left(2 \tan ^{-1}\left(\frac{t}{a}\right) \cos \left(s \tan ^{-1}\left(\frac{t}{a}\right)\right)-\log \left(a^2+t^2\right) \sin \left(s \tan ^{-1}\left(\frac{t}{a}\right)\right)\right) \, dt$$ using Mathematica.
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.