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| bio | website | |
|---|---|---|
| location | Washington, DC | |
| age | 59 | |
| visits | member for | 2 years, 2 months |
| seen | 13 hours ago | |
| stats | profile views | 277 |
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Jun 14 |
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Sum of Infinite Series with the Gamma Function It's the definition. The ratio of consecutive coefficients of the power series is a rational power of the power $n$, in this case it's $n^{-k}$. See en.wikipedia.org/wiki/Generalized_hypergeometric_function . |
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Jun 14 |
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Sum of Infinite Series with the Gamma Function In general, $\sum_{n=1}^\infty\frac{1}{\Gamma(n)^k} = \,_0F_{k-1}(;1,1,\dots,1;1)$ is a generalized hypergeometric function evaluated at $z = 1$. |
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Jun 10 |
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$\bigcup_{n}V_n$ is dense in $V$ implies $\bigcup_{n}L^2(0,T;V_n)$ is dense in $L^2(0,T;V)$? Think about a different approximating sequence if this one is too cumbersome. For example, Specifically, let $\varphi_n$ be an orthonormal basis of $L^2(0,T;\mathbb{R})$. Now consider the span of all $\varphi_j(\cdot)w_k$, where $j, \, k \le n$. |
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Jun 8 |
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Query on Brahmagupta-Fibonacci Identity Please explain how $p, q, r, a, n, b$ are related. |
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Jun 8 |
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Let $V$ be the set of all bounded solutions of the ODE: Suppose $u$ is a solution and $c_2 \ne 0$. Prove that $u$ is unbounded. Therefore $u \notin V$. Repeat this argument with $c_1$. Which solutions are therefore left in $V$? |
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Jun 6 |
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Show $\{f_n'(x)\}$ is uniformly bounded given that $\{f_n''(x)\}$ is and $f_n \rightarrow 0$ uniformly @AnonSubmitter85 - your edit gives a correct solution, and you can conclude more. Using your notation, set $x = a$ (arbitrary) and then choose $b$ such that $b - a = \sqrt{M/(4L_n)}$. The result is now $|f_n'(x)| \le 2 \sqrt{L_n \cdot M}$. This is known as Landau's Inequality. Therefore the $f_n'$ are not only uniformly bounded but go to $0$. |
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Jun 6 |
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Show $\{f_n'(x)\}$ is uniformly bounded given that $\{f_n''(x)\}$ is and $f_n \rightarrow 0$ uniformly Drop the subscript $n$ as it is irrelevant. Rewrite the first identity as $f'(a) = (f(b) - f(a))/(b-a) + (b-a)f''(c)/2$. At this point you are still free to choose $a$ and $b$. So choose any $a = x$, set $b = x+1$, and look at the result again. What can you conclude, using your assumptions? |
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Jun 5 |
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The order of the following equations Are you asking which number is the smallest and which is the largest? |
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Jun 4 |
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Show that a group homomorphism $f$ is the identity. So how can you describe all group homomorphisms of $\mathbb{Z}_7$? |
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Jun 4 |
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Show that a group homomorphism $f$ is the identity. Group homomorphism of $(\mathbb{Z}_7,+)$ or field homomorphism? |
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Jun 4 |
answered | How to prove (global) uniqueness of solution to linear, first order ODE? |
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Jun 3 |
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recurrence relationship $a_{n+2} = 4a_{n+1} - 2a_n$ for all $n \geq 0$ @WiseStrawberry - look up another example like this one and try to emulate what was done there. |
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Jun 2 |
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find an ODE for the travelling-wave solution I think this is discussed in Joel Smoller's book. |
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May 31 |
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A question on mean value inequality @Paul - set $\lambda_i = 1/n$ in the proofs that SYZ's comment links to in order to make the connection |
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May 29 |
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Sum of Random Variables… @ TestGuest - see my edit. |
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May 29 |
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Sum of Random Variables… responded to changed question |
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May 29 |
answered | Sum of Random Variables… |
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May 28 |
answered | Is $\sum_{n=1}^{\infty} {x^2 e^{-nx}}$ uniformly convergent in $[0,\infty)$ |
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May 27 |
answered | Hardness of a special case of maximum matching |
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May 26 |
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Show that there are $36$ $5$-Sylow subgroups Regarding your first question: Could a Sylow 5-group in $S_6$ have $5^2$ elements? Or $5^3$? Following up: How many different groups of order $5$ do you know? |
