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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/…
Jan
6
comment In dual numbers, what is the value of expressions $0^\varepsilon$ and $\varepsilon^{\varepsilon}$?
@epimorphic canonical embeeding is through the use of 2x2 matrices.
Jan
6
comment In dual numbers, what is the value of expressions $0^\varepsilon$ and $\varepsilon^{\varepsilon}$?
@epimorphic i - complex unity, j - split-complex unity, ϵ′ - alternative dual unity.
Jan
4
comment Are these identities Newton series?
@Lucian $\binom {-1}{m}=(-1)^m$. Thus $(-1)^{m-k}$ under second sum becomes $(-1)^k$...
Jan
4
comment How it comes that integral of odd function is not even?
@user2345215 not necessary.
Jan
4
comment How it comes that integral of odd function is not even?
@user2345215 $1/z$ is an odd function, following the definition of odd functions. Function cannot be odd on an interval.
Jan
4
comment Does Euler-Mascheroni constant belong to the ring of periods?
Regarding $e$, it is clear not a period, there is little doubt. Not the case with $\gamma$ though. Even more than $\gamma$, $e^{-\gamma}$ is likely to be a period.
Jan
4
comment Does Euler-Mascheroni constant belong to the ring of periods?
Expected by whom not to be period?
Jan
1
comment There is a subset of positive integers which no computer program can print
By postulating that all red numbers is a set u are using axiom of choice.
Dec
29
comment Is there a symbol for integrating and setting $C=0$?
...Good example! And natural integral of it is neither of your two, it is $-\frac12 \cos(2x)$ wolframalpha.com/input/…
Dec
28
comment Is there a symbol for integrating and setting $C=0$?
@fvel follow the link and insert 2x in the formula. wolframalpha.com/input/… And look at the result. U can insert any function and if the expression converges, u will receive the result in the "result" field
Dec
28
comment Is there a symbol for integrating and setting $C=0$?
@fvel there are two formulas there, one uses Fourier transform, the other uses Newton series. You can also use pre-made tables or Wolfram Alpha: wolframalpha.com/input/… . (replace sin(x) with a function u want)
Dec
28
comment Is there a symbol for integrating and setting $C=0$?
@fvel You can take any function with constant term and make from it a function without a constant term by simple operations. For instance, $\frac {x^3}3+2x+C=C(\frac{x^3}{3C}+\frac {2x}C+1)$
Dec
28
comment Is there a symbol for integrating and setting $C=0$?
@fvel and what antiderivative you want? Any? Do u consider constant term is zero in $\ln ax$? Note that $\ln ax = \ln x + \ln a$. You can take any function with constant term and make from it a function without a constant term.
Dec
28
comment Is there a symbol for integrating and setting $C=0$?
@fvel it is unclear what u want mathematically. If you want the antiderivative to be 0 in x=0, use integral from 0. The integral of 1/x is discontinuous in 0, so u choose a constant some other way. For instance, you can integrate from 1, then you will have $\ln x$. From the point of view of nature, though $\ln |x|+\gamma=\ln|x e^\gamma|$ is more natural (note that you can remove the constant by some elementary algebraic manipulations), so to get natural integral in a form without constant term, like $\ln|x e^\gamma|$.
Dec
28
comment Is there a symbol for integrating and setting $C=0$?
@fvel For polynomials the first formula (integral from zero) will allways produce the same result as natural integral.