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Mathematics

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earned this badge 13 times.
A System of Simultaneous Pell Equations
Awarded May 4, 2018 at 13:24
Proving that $\lim_{x\to1^-}\left(\sqrt[a]{1-x}\cdot\sum_{n=0}^\infty~x^{n^a}\right)=\Gamma\left(1+\frac1a\right)$
Awarded Aug 30, 2017 at 4:10
Evaluating $\prod_p(1\pm\frac{4}{p^2})$ in Closed Form
Awarded Feb 25, 2017 at 10:51
Evaluating $~\int_0^1\sqrt{\frac{1+x^n}{1-x^n}}~dx~$ and $~\int_0^1\sqrt[n]{\frac{1+x^2}{1-x^2}}~dx$
Awarded Nov 23, 2016 at 5:53
Closed Form for $~\lim\limits_{n\to\infty}~\sqrt n\cdot(-e)^{-n}\cdot\sum\limits_{k=0}^n\frac{(-n)^k}{k!}$
Awarded Jun 15, 2016 at 8:41
Proving $~\prod~\frac{\cosh\left(n^2+n+\frac12\right)+i\sinh\left(n+\frac12\right)}{\cosh\left(n^2+n+\frac12\right)-i\sinh\left(n+\frac12\right)}~=~i$
Awarded Mar 26, 2016 at 11:23
Elegantly Proving that $~\sqrt[5]{12}~-~\sqrt[12]5~>~\frac12$
Awarded Mar 23, 2016 at 10:37
Proving that $\int_0^\infty\frac{J_{2a}(2x)~J_{2b}(2x)}{x^{2n+1}}~dx~=~\frac12\cdot\frac{(a+b-n-1)!~(2n)!}{(n+a+b)!~(n+a-b)!~(n-a+b)!}$
Awarded Jan 20, 2016 at 16:00
Closed Form for $~\int_0^1\frac{\text{arctanh }x}{\tan\left(\frac\pi2~x\right)}~dx$
Awarded Jul 20, 2015 at 12:13
Irreducibility of $~\frac{x^{6k+2}-x+1}{x^2-x+1}~$ over $\mathbb Q[x]$
Awarded Jan 31, 2015 at 11:08
Proving that $\int_0^\infty\Big(\sqrt[n]{1+x^n}-x\Big)dx~=~\frac12\cdot{-1/n\choose+1/n}^{-1}$
Awarded Nov 8, 2014 at 13:54
Closed Form for the Imaginary Part of $\text{Li}_3\Big(\frac{1+i}2\Big)$
Awarded Sep 19, 2014 at 16:41
Evaluating $\int_0^{2\pi}\frac{dt}{\sqrt[4]{P(\cos t,\sin t)}}$
Awarded Jun 7, 2014 at 18:10

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