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2d
revised Is $(1+2+3+…)=(1+2+2^2+2^3+…)(1+3+3^2+…)(1+5+5^2+…)…$?
added 243 characters in body
Apr
18
answered Is $(1+2+3+…)=(1+2+2^2+2^3+…)(1+3+3^2+…)(1+5+5^2+…)…$?
Apr
15
comment Does this integral have any closed form? $\displaystyle\int\frac{1}{x+\sin(x+1)}\mathop{\mathrm dx}$
Can you provide details? Assuming the material on those two pages, what are the steps to apply them to this particular integral?
Apr
14
answered Radius of convergence of ${\sum_{n=0}^{\infty}} \frac{z^{2n}}{4^n}$
Apr
11
comment integral of a sequence
Your conclusion seems to be defective.
Apr
3
comment Show the outer measure of a union is the sum of the measures without Caratheodony
@Ellya: perhaps that is what Kiley means by "Caratheodory"---he didn't say.
Apr
3
comment Integrate a sign function wrt probability measure
Subdivide $\mathbb R$ into a few sets, determined by whether $x<a, x=a, x>a$ and by whether $x<b, x=b, x>b$.
Apr
2
comment Cardinalities of bases of a free $R$ module are same?
How about using "we" to mean "the writer and the reader"? I think Zhen's objection is frivolous.
Apr
2
comment How do I find contour integral with no poles?
"Contour" means simple closed curve, in this case. So $(0,1)$ won't help if it is supposed to be a contour integral.
Apr
2
comment Show that $ \mathbb{E}[X] < \infty \Longleftrightarrow \sum_{n=1}^\infty \mathbb{P}[X>n] < \infty $ for random variable $X$
Say for example $X$ is the constant $1$. Then $\mathbb E[X]=1$ and $\sum_{n=1}^\infty \mathbb{P}[X>n] = 0$. Although they are not equal, they are both $< \infty$
Apr
2
comment Is it jusfied then to say $\mathbb R$ the splitting field of $x^2-1$ over $\mathbb R?$
From now on I'm not trying to remember the numbers, just calling all those guys user12345. If they want to be remembered, they should choose a user name.
Apr
2
comment Is it jusfied then to say $\mathbb R$ the splitting field of $x^2-1$ over $\mathbb R?$
So, user12345 is right, and Gallion's definition is incomplete.
Apr
2
answered Prove $\frac1T \int_0^T\left(\sum_{k=-\infty}^{\infty}c_ke^{j{\frac{2\pi kt}{T}}}\right)^2dt= \sum_{k=-\infty}^{\infty}|c_k|^2$
Apr
2
comment A question on limit of weak-* convergence of probability measures
Then take $[0,1]$ with Lebesgue, and $Y_i = [\frac{1}{2} - \frac{1}{i}, \frac{1}{2} + \frac{1}{i}]$. Of course you can do something like this to get a singular measure as the limit, as well.
Apr
1
reviewed Approve suggested edit on Simplification question regarding a quotient
Mar
31
comment How can I calculate the following Lebesgue integral $\int_{-\infty}^{\infty}||x|^{-0.35}-|x-1|^{-0.35}|^{1.8} d\lambda(x)$
Find asymptotics at $-\infty$ at $0$ at $1$ and at $+\infty$. Examine convergence in each of these cases.
Mar
31
answered Real world situation with System of Equation with 3 variables?
Mar
31
comment Integrate with square root in square
You need to get $dx$ only in terms of $t$ and $dt$. That's why I solved for $x$ first.
Mar
31
answered Integrate with square root in square
Mar
31
comment Integrate with square root in square
No, much simpler than that.