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Jul
27
awarded  Popular Question
Jul
2
awarded  Curious
Apr
19
comment Compute $I=\int_0^{+\infty}\frac{\arctan(t)}{e^{\pi t}-1}dt$
Nice answer. This is the second Binet's formula
Apr
6
revised Prove $\int_{0}^\infty \frac{1}{\Gamma(x)}\, \mathrm{d}x = e + \int_0^\infty \frac{e^{-x}}{\pi^2 + \ln^2 x}\, \mathrm{d}x$
added 1 characters in body
Apr
6
answered Prove $\int_{0}^\infty \frac{1}{\Gamma(x)}\, \mathrm{d}x = e + \int_0^\infty \frac{e^{-x}}{\pi^2 + \ln^2 x}\, \mathrm{d}x$
Apr
5
comment Prove $\int_{0}^\infty \frac{1}{\Gamma(x)}\, \mathrm{d}x = e + \int_0^\infty \frac{e^{-x}}{\pi^2 + \ln^2 x}\, \mathrm{d}x$
As far as I know(from the book "Mathmatical Constant" of S.R.Finch, p263-p264), this formula was discovered by Ramanujan. Hardy proved a generalized version of this formula in his paper "Another formula of Ramanujan", J.London Math.Soc. (1937) s1-12 (4): 314-318.
Apr
4
awarded  Nice Answer
Apr
3
suggested suggested edit on Demonstrate that $\displaystyle \frac{(2n - 2)!!}{(2n - 3)!!} \simeq 1.7 \sqrt{n}$
Mar
30
comment Help in finding a definite integral
Gamma function may help you.
Mar
29
revised sum of three cubes and parametric solutions
[Edit removed during grace period]
Mar
29
revised sum of three cubes and parametric solutions
added 266 characters in body
Mar
26
awarded  Yearling
Mar
5
awarded  Necromancer
Feb
19
answered How to prove $\int_0^1\tan^{-1}\left[\frac{\tanh^{-1}x-\tan^{-1}x}{\pi+\tanh^{-1}x-\tan^{-1}x}\right]\frac{dx}{x}=\frac{\pi}{8}\ln\frac{\pi^2}{8}?$
Dec
9
comment Different methods to prove $\zeta(s)=2^s\pi^{s-1}\sin\left(\frac{s\pi}{2}\right) \Gamma (1-s) \zeta (1-s)$.
The book "the Theory of Riemann zeta function" by Titchmarsh contains several proofs of the functional equation.
Dec
2
comment Baby rudin chapter 6 exercise 14 ---Isn't it a typo?
Second mean value theorem for integration
Dec
1
answered If $\sum_{n=1}^\infty na_n$ converges , does $\sum_{n=1}^\infty na_{n+1}$ converge?
Nov
29
comment if the matrix such $B-A,A$ is Positive-semidefinite,then $\sqrt{B}-\sqrt{A}$ is Positive-semidefinite
I wonder whether $A$ is positive definite.
Nov
29
awarded  Organizer
Nov
29
revised How find this limit $\lim_{n\to\infty}\frac{x_{n}}{n}=?$
improved formatting