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 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/… Jan6 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. Jan6 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. Jan4 comment Are these identities Newton series? @Lucian $\binom {-1}{m}=(-1)^m$. Thus $(-1)^{m-k}$ under second sum becomes $(-1)^k$... Jan4 comment How it comes that integral of odd function is not even? @user2345215 not necessary. Jan4 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. Jan4 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. Jan4 comment Does Euler-Mascheroni constant belong to the ring of periods? Expected by whom not to be period? Jan1 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. Dec29 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/… Dec28 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 Dec28 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) Dec28 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, $\frac {x^3}3+2x+C=C(\frac{x^3}{3C}+\frac {2x}C+1)$ Dec28 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. Dec28 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 $\ln|x e^\gamma|$. Dec28 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.