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answered How to evaluate $\lim _{n\to \infty }\:\int _{1/(n+1)}^{1/n}\:\frac{\sin\left(x\right)}{x^3}\:dx$?
Apr
13
awarded  Nice Answer
Apr
12
comment Find the closed form of $\int_0^{\large \frac{\pi}{2}}\frac{x^{2n}\cdot\log{{\sin{x}}}}{\sin^{2n}{x}}dx, \space n\ge 1$
@ClaudeLeibovici Yeah, true. I'm pretty often in chat. :-)
Apr
12
asked Find the closed form of $\int_0^{\large \frac{\pi}{2}}\frac{x^{2n}\cdot\log{{\sin{x}}}}{\sin^{2n}{x}}dx, \space n\ge 1$
Apr
12
comment How to solve $\int_0^{\frac{\pi}{2}}\frac{x^2\cdot\log\sin x}{\sin^2 x}dx$ using a very cute way?
@OlivierOloa anyway
Apr
3
comment $\lim_{n\to\infty} \frac{1}{\log(n)}\sum _{k=1}^n \frac{\cos (\sin (2 \pi \log (k)))}{k}$
@Lucian Nice to meet you. :-) Are you a student, a professor?
Apr
3
comment $\lim_{n\to\infty} \frac{1}{\log(n)}\sum _{k=1}^n \frac{\cos (\sin (2 \pi \log (k)))}{k}$
@Lucian Yeap. A self-educated one, not a product in any way of the educational system from my country. Are you Romanian?
Apr
3
accepted $\lim_{n\to\infty} \frac{1}{\log(n)}\sum _{k=1}^n \frac{\cos (\sin (2 \pi \log (k)))}{k}$
Apr
3
revised $\lim_{n\to\infty} \frac{1}{\log(n)}\sum _{k=1}^n \frac{\cos (\sin (2 \pi \log (k)))}{k}$
added 12 characters in body
Apr
3
comment $\lim_{n\to\infty} \frac{1}{\log(n)}\sum _{k=1}^n \frac{\cos (\sin (2 \pi \log (k)))}{k}$
@downvoters, I said "tools", not solutions.
Apr
3
asked $\lim_{n\to\infty} \frac{1}{\log(n)}\sum _{k=1}^n \frac{\cos (\sin (2 \pi \log (k)))}{k}$
Mar
26
comment Aproximation of $a_n$ where $a_{n+1}=a_n+\sqrt {a_n}$
+1 A far nicer answer.
Mar
22
awarded  Nice Question
Mar
17
comment Finding the closed form of $\sum_{k=1}^{\infty} \sum_{n=1}^{\infty}(-1)^{k+n} \frac{\log(k+n)}{k n}$
@Lucian And it's particularly nice when trying to compute it by series manipulation only.
Mar
17
comment Finding the closed form of $\sum_{k=1}^{\infty} \sum_{n=1}^{\infty}(-1)^{k+n} \frac{\log(k+n)}{k n}$
@Lucian The series $\sum_{k=1}^{\infty} \sum_{n=1}^{\infty}(-1)^{k+n} \frac{\log(k+n)}{k+ n}$ is one of the most beautiful series I ever computed. I liked it so much that I also dedicated some study to other similar forms of it.
Mar
16
comment Finding the closed form of $\sum_{k=1}^{\infty} \sum_{n=1}^{\infty}(-1)^{k+n} \frac{\log(k+n)}{k n}$
@Lucian I see your point, and partially I agree, but studying similar forms of some series that have closed forms might be interesting, at least to me. I wouldn't like to only study things I believe they have a closed form since I might be wrong in many cases. Besides that, finding integrals and series without closed forms seems to be by far a great challenge.
Mar
16
comment Finding the closed form of $\sum_{k=1}^{\infty} \sum_{n=1}^{\infty}(-1)^{k+n} \frac{\log(k+n)}{k n}$
(+1) Thank you for trying that. I worked on that for a while but I didn't get anything satisfactory.
Mar
16
comment Integration: Branch cuts
For the power of contour integration (+1).
Mar
16
comment Integration: Branch cuts
@Lucian I get $\approx 1.382763392139544$.
Mar
16
comment Integration: Branch cuts
@Lucian I took this form of answer from Mathematica and numerically things seem correct.