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Y. Zhao's user avatar
Y. Zhao's user avatar
Y. Zhao's user avatar
Y. Zhao
  • Member for 12 years, 11 months
  • Last seen this week
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Top posts
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question
84
A hard integral identity on MathSE
Jan 18, 2014
question
42
A mysterious connection between Ramanujan-type formulas for $1/\pi^k$ and hypergeometric motives
Sep 12, 2017
answer
15
Why do Pell equations appear in Ramanujan's pi formulas?
Dec 8, 2014
question
15
sum of three cubes and parametric solutions
Apr 1, 2013
answer
13
show that $ \frac{\Gamma(\frac{1}{24})\Gamma(\frac{11}{24})}{\Gamma(\frac{5}{24})\Gamma(\frac{7}{24})} = \sqrt{3}\cdot \sqrt{2 + \sqrt{3}} $
Sep 9, 2016
question
12
Failing of heuristics from circle method
Sep 7, 2014
question
12
Congruence equation and quadratic residue
Jun 19, 2016
answer
11
Ramanujan's series for $(1/\pi)$ and modular equation of degree $29$
Mar 11, 2015
question
10
Question about Nyman-Beurling-Baez-Duarte Equivalent for Riemann Hypothesis
Nov 19, 2011
question
10
A question on Ramanujan's $1/\pi$ formulas
Aug 28, 2015
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80
Two curious "identities" on $x^x$, $e$, and $\pi$
28
How to prove $\int_0^1\tan^{-1}\left[\frac{\tanh^{-1}x-\tan^{-1}x}{\pi+\tanh^{-1}x-\tan^{-1}x}\right]\frac{dx}{x}=\frac{\pi}{8}\ln\frac{\pi^2}{8}?$
14
Prove $\int_{0}^\infty \frac{1}{\Gamma(x)}\, \mathrm{d}x = e + \int_0^\infty \frac{e^{-x}}{\pi^2 + \ln^2 x}\, \mathrm{d}x$
9
Square-free value of $n^2+1$ without large prime factors
8
Prove $\sum_{i=1}^{n}\frac{x_{i}^3}{x_{i+1}^2}\geq \sum_{i=1}^{n}\frac{x_{i}^2}{x_{i+1}}$