meta user
network profile
| bio | website | ondrejcertik.com |
|---|---|---|
| location | Reno, NV | |
| age | 29 | |
| visits | member for | 1 year |
| seen | yesterday | |
| stats | profile views | 30 |
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May 9 |
awarded | Yearling |
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Feb 25 |
awarded | Nice Question |
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Jan 16 |
awarded | Commentator |
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Jan 16 |
comment |
Is odd continuous function differentiable at $x=0$? @N.S. Please do, I didn't want to put your solution into answers myself. |
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Jan 16 |
comment |
Solution of functional equation $f(x/f(x)) = 1/f(x)$? Very nice! So if the function $f(x)$ is analytic, then you prove that $f(x)=1$. Assuming only that $f(x)$ is continuous, then the only possible other solutions are not analytic. That helps a lot. |
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Jan 16 |
comment |
Solution of functional equation $f(x/f(x)) = 1/f(x)$? Right. So the domain of $g(x)$ must be an interval (e.g. not a union of two disjoint intervals). However, what if we only solve this on an interval [1, 10], let's say? I guess we would run into some contradictions with domains and ranges in the functional equation. |
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Jan 16 |
comment |
Solution of functional equation $f(x/f(x)) = 1/f(x)$? Because $g(x)=1/x$ is also a solution of $g(g(x))$ and somehow it got eliminated. So something is not right. (Of course, it would get eliminated later anyway due to $g'(0)=1$, but that's not the point.) |
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Jan 16 |
revised |
Solution of functional equation $f(x/f(x)) = 1/f(x)$? added 969 characters in body |
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Jan 16 |
awarded | Editor |
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Jan 16 |
revised |
Solution of functional equation $f(x/f(x)) = 1/f(x)$? Grammar. |
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Jan 16 |
asked | Solution of functional equation $f(x/f(x)) = 1/f(x)$? |
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Jan 16 |
comment |
Is odd continuous function differentiable at $x=0$? N.S., you are right! $\frac{f(x)}{x} = \sin\frac{1}{x^2}$ which oscillates between -1 and 1 and so the limit does not exist. So this function is not differentiable at $x=0$. Thanks! |
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Jan 16 |
asked | Is odd continuous function differentiable at $x=0$? |
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Oct 25 |
awarded | Tumbleweed |
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Oct 18 |
asked | Conditions on $p(x)$ and $q(x)$ in energy scalar product |
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Oct 10 |
asked | How to prove Gegenbauer's addition theorem? |
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Sep 21 |
awarded | Scholar |
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Sep 21 |
accepted | How to prove asymptotic limit of an incomplete Gamma function |
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Sep 21 |
comment |
How to prove asymptotic limit of an incomplete Gamma function I verified your steps, I think it's all correct. I am accepting your answer as it gives a simple proof. |
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Sep 21 |
comment |
How to prove asymptotic limit of an incomplete Gamma function Thanks! As a matter of fact, I actually wanted to prove that $\gamma(z, x)\over\Gamma(z)$ goes to zero, but thought it'd be easier to do it with the upper incomplete gamma function. |
