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18m
comment How do i evaluate this integral $ \int_{\pi /4}^{\pi /3}\frac{\sqrt{\tan x}}{\sin x}dx $?
The integral from $\frac\pi4$ to $\frac\pi2$ has a nice form, but $\frac\pi3$ does not seem to have such a nice form.
19h
revised Closed form for a binomial series
add proof of $(2)$
19h
revised Closed form for a binomial series
add proof of $(2)$
21h
revised Closed form for a binomial series
fix typo
21h
revised Closed form for a binomial series
add the second answer
21h
revised Closed form for a binomial series
add the definition of $H_n^{(2)}$
21h
answered Closed form for a binomial series
22h
awarded  Necromancer
1d
comment Deriving expression for an integral that arose in Fourier analysis.
$z_t(\omega) = \int_{-\omega}^{\omega}F(\omega)e^{i\omega t}d\omega$ uses $\omega$ as a dummy variable and a parameter. This can cause confusion.
1d
awarded  Revival
1d
revised Is integration of $x\operatorname{cosec}(x)$ defined?
add a link to the Dilogarithm Function
1d
answered Binomial Sum: Values
1d
comment How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$?
@goblin: it does. It is even stated so: "Furthermore, since $\cos(x)$ is continuous near $0$ and $\cos(0) = 1$, we get that..." Is that a problem? This limit is not required to show the continuity of $\cos(x)$. For that, we only need $$\lim_{x\to0}\sin(x)=0$$ since $$\cos(x)-\cos(y)= -2\sin\left(\frac{x+y}2\right) \sin\left(\frac{x-y\vphantom{+}}2\right)$$
1d
revised Is integration of $x\operatorname{cosec}(x)$ defined?
shorten the derivation by skipping the integration by parts
1d
answered Is integration of $x\operatorname{cosec}(x)$ defined?
1d
revised Convergence of a sequence of non-negative real numbers $x_n$ given that $x_{n+1} \leq x_n + 1/n^2$.
simplify the argument
1d
answered Convergence of a sequence of non-negative real numbers $x_n$ given that $x_{n+1} \leq x_n + 1/n^2$.
1d
revised Showing that $x^{11} \equiv 5 \pmod{47}$ has only solution $x \equiv 15$.
add a bit on solving the Diophantine equation
1d
revised Showing that $x^{11} \equiv 5 \pmod{47}$ has only solution $x \equiv 15$.
solve for $x$
1d
revised Showing that $x^{11} \equiv 5 \pmod{47}$ has only solution $x \equiv 15$.
improve the explanation