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 Pundit
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Apr
16
comment Is the product of all objects of a finite category an initial object?
What are the left and right projections out of $x\times x$ here? Once they are fixed, I feel I can always find a diagram so that it doesn't work out.
Apr
15
comment Second order PDE
You have seen proper formula formatting alla $\frac{{\mathrm d}y}{{\mathrm d}x}$ in edits of your other questions - why don't you apply the knowledge?
Apr
10
comment Integrability in Ito isometry
I read the article and came to the same question. Have you clarified it in the last 2 years? If there's something to share, you could write an answer and edit the Wikipedia page.
Apr
10
comment Explicit formula from this recursive formula?
$a_n=(n+1)!\left(a_0+\sum_{k=2}^{n+1}(1-\frac{1}{k})\right)$
Apr
10
revised Explicit formula from this recursive formula?
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Apr
9
revised Closed form of the sum $\sum\limits_{n=0}^\infty \exp(-n^3)$
added 51 characters in body
Apr
9
revised Closed form of the sum $\sum\limits_{n=0}^\infty \exp(-n^3)$
added 62 characters in body
Apr
9
revised Closed form of the sum $\sum\limits_{n=0}^\infty \exp(-n^3)$
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Apr
9
answered Closed form of the sum $\sum\limits_{n=0}^\infty \exp(-n^3)$
Apr
1
awarded  Pundit
Mar
23
comment What is a Manifold?
@Danu: Why is that a plus? A physics-point of view was explicitly asked for.
Mar
19
comment What is a Manifold?
A space in which you can formulate laws of motion of quantities within it - laws which are equivalently valid from an infinite family of perspectives, which are smoothly related.
Mar
19
comment Convergence of $\sum_n \frac{n!}{n^n}$
I also don't think that's instantly immediate for which n this works, or why exactly $n^2$ pops up. It calls for a proof by induction.
Mar
17
accepted Does this property characterize monomorphisms?
Mar
16
asked Does this property characterize monomorphisms?
Mar
9
awarded  Popular Question
Mar
6
comment Sequence from generating function $\frac{1}{(1 - \frac{x}{3})^2}$
Btw. you can always use a software like WolframAlpha.com, which will quickly tell you that, more generally, $\frac{1}{\left(1+\tfrac{x}{a}\right)^b}$ expands as $\sum_{n\ge 0}\left(\prod_{k=0}^n\left(1+\frac{b-1}{k}\right)\right)\frac{1}{a^k}\,x^k$.
Mar
6
comment Sequence from generating function $\frac{1}{(1 - \frac{x}{3})^2}$
@Superian007: I'm not sure what you mean. To spell it out more, you know that $\frac{1}{1-z}=\sum_{n\ge 0}z^n$ and then either the approach $\frac{1}{(1-z)^2}=\frac{\partial}{\partial z}\frac{1}{1-z}$ or $\frac{1}{1-z}\,f(z)=\sum_{n=0}^\infty\left(\sum_{k=0}^n a_k\right)z^k$ tells you that $\frac{1}{(1-z)^2}=\sum_{n\ge 0}n\,z^n$. Now set $z=\frac{x}{3}$.
Mar
6
answered Sequence from generating function $\frac{1}{(1 - \frac{x}{3})^2}$
Mar
3
revised Subgroup of $G=\langle(123),(456),(23)(56)\rangle$
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