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Mathematics
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Z Ahmed's user avatar
Z Ahmed
  • Member for 5 years, 7 months
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  • India
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question
20
Integral $\int_{-\infty}^{\infty} \arctan(e^x) \arctan(e^{-x})dx=\frac{7}{4}\zeta(3)$
Jun 17, 2019
answer
19
Evaluate $\int_{0}^{\infty} \frac{\sin x-x\cos x}{x^2+\sin^2x } dx$
Jul 21, 2019
answer
15
Integrate $\int_{0}^{\pi} \frac{1}{1+3^{\cos x}} dx.$
Feb 5, 2020
question
15
Proving that $\sum_{k=0}^{n}\frac{(-1)^k}{{n\choose k}}=[1+(-1)^n] \frac{n+1}{n+2}.$
Jun 5, 2019
question
13
Proving $\sin(\tanh x) \ge \tanh(\sin x)$, for $x \in [0,\pi/2]$
Mar 30, 2020
question
13
A simple proof for Glasser: $\int_{-\infty}^{\infty} f(x-a/x) dx=\int_{-\infty}^{\infty} f(x) dx, a>0$
Dec 13, 2020
answer
11
Evaluate $\iiint_{[0,1]^3}\frac{dx\,dy\,dz}{(1+x^2+y^2+z^2)^2}$
Jul 25, 2019
question
10
Proving $\int_{0}^{1} \frac{\tanh^{-1}\sqrt{x(1-x)}}{\sqrt{x(1-x)}}dx=\frac{1}{3}(8C-\pi\ln(2+\sqrt{3}))$ for an identity of Srinivasa Ramanujan
Aug 23, 2020
question
10
A dig at Ramanujan's: $\sum_{k=1}^{\infty} (-1)^{k-1} \frac{x^{pk}}{k(k!)^p} \sim p \ln x +p \gamma,~ p>0$
Mar 2, 2021
question
10
An interesting binomial summation
Jun 18, 2021