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A duck walks into a bar. Animal control is promptly called and the duck is released into a near by park.

My email is to be found on my website.


1d
comment Is there something special about 2015?
@DavidH: I can't figure out if this is constructive. Is uninteresting "not interesting", or is interesting "not uninteresting"? I assume the former, and interesting-ness would be captures by the existence of a formula with some general upper bound in length.
Jan
22
answered What is a quick way to establish that $\sum_{n=1}^\infty \frac {\log n}{n^{3/2}}$ converges?
Jan
22
comment Does $\int_0^\infty e^{-x}\sqrt{x}dx$ converge?
@dalastboss: k, thx. Though I have no real intuition for the ratio test, I don't know if I consider that an argument. I mean we know it's true from the start and so we already know there is a proof when asking. The task is to get to the level where the opposite statement feels wrong :)
Jan
22
revised Physically, what meaning have Taylor series which have their lower order terms equal to zero, but their higher order terms non zero?
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Jan
21
answered Physically, what meaning have Taylor series which have their lower order terms equal to zero, but their higher order terms non zero?
Jan
21
comment Why's the derivative of $f(x) = x^3-5x-2 $ not $3x^2-7$?
To see why the derivative of a constant function is zero, you should think about the interpretation of the derivative.
Jan
21
comment Integrate this monster
Is the $\psi$ even relevant? You can absorb the b/g term into the sum and make the "int exp sum" a "prod int exp" and rescale the g to get rid of lambda. But then the problem is then the keeping track of convergence. In fact it didn't converge in Mathematica for and of the values I tries. Btw. where does this come from? Can you give one examples for $\{a,b,\psi,\{t_i\},\{l_i\}\}$ for which one could try and solve it directly?
Jan
20
answered Determine if it converges or diverges : $\sum_{n=1}^{\infty} \frac {2^n \cdot n!}{1\cdot2\cdots (2n-1)}\cdot \frac{1}{\sqrt{2n+1}}$
Jan
20
comment Does $\int_0^\infty e^{-x}\sqrt{x}dx$ converge?
It's a value of the Gamma function, $\Gamma(\tfrac{3}{2})$. To me, an nice answer would be an argument why $\int_0^\infty {\mathrm e}^{-x}x^a\,{\mathrm d}x$ converges for any $a>0$. The problem is that the factorial already grows so fast, it's hard to find a reasonable upper bound. You can do integration under the integral tricks, but that raises more questions and hence isn't too smooth.
Jan
20
comment What are conditions for an infinite sum with a complex parameter not to be analyitically extendable?
@achillehui: Thanks for the responds. Okay, it seems the Fabry theorem is actually formulated for $z^{f(n)}$ instead of ${\mathrm e}^{-z\,f(n)}$ so one has to reformulate it a bit. In any case, do you know any "function with a known name" which fits?
Jan
20
asked What are conditions for an infinite sum with a complex parameter not to be analyitically extendable?
Jan
19
revised Explicit analytic continuation of the zeta function and shift operators
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Jan
18
asked Explicit analytic continuation of the zeta function and shift operators
Jan
18
comment The obivious “why”-questions
@amWhy Why Why?
Jan
16
comment slightly different definition of an ordered pair
I assume the Wikipedia page on the ordered pair, especially the subsection here should answer your question, or at least lead to another one.
Jan
16
comment The ring of formal power series
The evaluation function will just lack the point $X=\tfrac{1}{q}$ in it's domain.
Jan
16
comment Prove that a statement or its negation follows from ZFC
Doesn't this follow for all unproven sentences from the completeness theorem for first order logic together with the law of excluded middle?
Jan
15
comment Approximating $a = bx + cx^2 + O(x^3)$
@user3183724: Smells like computing partition functions of gases in statistical mechanics, btw.
Jan
15
revised Approximating $a = bx + cx^2 + O(x^3)$
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Jan
15
comment Approximating $a = bx + cx^2 + O(x^3)$
@user3183724: I've expanded the root in your small paramerter $a$ up to the second order, and then did the same for ${\mathcal O}(z^3)$. See i.imgur.com/WKoGC9V.png.