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awarded  Good Answer
Aug
19
comment Series representation for $L=\frac{3}{2} \sqrt{4 \pi ^2 A^2+W^2}-\frac{\sqrt{5 W \sqrt{4 \pi ^2 A^2+W^2}+6 \pi ^2 A^2+3 W^2}}{\sqrt{2}}$
Uhh... you could try computing the derivatives of W wrt L to construct the Taylor series. (And by you I mean Mathematica)
Aug
19
answered Initial value problem with a delta term
Aug
19
comment How find this integral $I=\int_{0}^{1}\int_{0}^{1}\frac{\ln{(1+xy)}}{1-xy}dxdy$
@Tunk-Fey I think the best way would be to use the two-dilog functional identity $\frac{\text{Li}_2{(-z)}}{1+z}=\frac{\zeta{(2)}-\ln{(-z)}\ln{(1+z)-\operatorname‌​{Li}_2{(1+z)}}}{1+z}$ to split up the integrand into three bite-size morsels. None of the resulting integrals seem too difficult after that.
Aug
19
comment A closed form for $\int_0^1{_2F_1}\left(-\frac{1}{4},\frac{5}{4};\,1;\,\frac{x}{2}\right)^2dx$
+1) Very nice. I had the exact same work up to the evaluation of the final limit via L'Hopital, which for some reason kept coming out wrong so I gave up. Question: did you know all those references off the top of your head or did you have to hunt them down? They look incredibly useful.
Aug
18
comment Why doesn't this converge?
@user157227 <<puts on physicist cap>> On the contrary! Symmetry is best way to integrate. <<puts mathecist cap back on>> Then again, we should probably prove that.
Aug
18
comment How find this integral $I=\int_{0}^{1}\int_{0}^{1}\frac{\ln{(1+xy)}}{1-xy}dxdy$
@Tunk-Fey I'm sorry, I'm not sure what exactly you're referring to. Are you asking how to evaluate $\int_{0}^{1}\frac{\text{Li}_2(-\alpha)}{1+\alpha}\mathrm{d}\alpha$? Or do you mean something else?
Aug
18
answered How find this integral $I=\int_{0}^{1}\int_{0}^{1}\frac{\ln{(1+xy)}}{1-xy}dxdy$
Aug
18
comment prove equilateral triangle
@qsmy You're quite welcome. Note that I just edited my response to include a minor correction.
Aug
18
revised prove equilateral triangle
minor correction
Aug
18
answered prove equilateral triangle
Aug
18
comment Is there a name for this point?
This seem pretty much analogous to finding the center of mass of three point particles.
Aug
18
comment System of non-linear equations.
Here's a rule of thumb: if the exponents in a problem are roughly equal to the current calendar year, then the answer to the problem is probably deceptively simple.
Aug
18
comment What's so special about binomial coefficients that someone decided to organize them in a triangle?
The Pascal's triangle Wikipedia page povides a decent abridged history of its development.
Aug
18
comment finding $\lambda$ when equation of parabola is given
Have you computed the discriminant of the equation yet?
Aug
18
comment Finding the value of trigonometric function of any angle?
@Ian It should probably be pointed out that there is only such a procedure for some rational multiplies of $\pi$, specifically the rational multiplies corresponding to increments of $3^\circ$ (and repeated bisection of these angles). But it can't be used to calculate, say, sine of $1^\circ=\frac{\pi}{180}$ and $2^\circ=\frac{\pi}{90}$
Aug
18
comment Prove that $\frac{{-\cos(x-y)-\cos(x+y)}}{-\cos(x-y)+\cos(x+y)} = \cot x \cot y$
@Mickey No. Read the formulas again more carefully.
Aug
17
comment Non linear ordinary differential equation
I doubt an exact solution exists.
Aug
17
answered Prove that $\frac{{-\cos(x-y)-\cos(x+y)}}{-\cos(x-y)+\cos(x+y)} = \cot x \cot y$
Aug
17
answered Interval of existence of a certain first-order ODE