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Mathematics
Dennis Orton's user avatar
Dennis Orton's user avatar
Dennis Orton's user avatar
Dennis Orton
  • Member for 4 years, 4 months
  • Last seen more than 1 year ago
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15
Evaluating the challenging sum $\sum _{k=1}^{\infty }\frac{H_{2k}}{k^3\:4^k}\binom{2k}{k}$.
Oct 18, 2020
12
Evaluating the challenging sum $\sum _{k=1}^{\infty }\frac{H_{2k}}{k^3\:4^k}\binom{2k}{k}$.
Oct 18, 2020
12
Challenging problem: Find $a$ where $\int_0^\infty \frac{\cos(ax)\ln(1+x^2)}{\sqrt{1+x^2}}dx=0$.
Jul 24, 2020
10
Evaluate $\int _0^{\infty }\frac{\ln \left(x^5+1\right)}{x^2+1}\:dx$ with real methods
May 15, 2020
10
Evaluating $\sum _{k=1}^{\infty }\frac{H_k}{4^k\left(2k+1\right)}\binom{2k}{k}$.
Oct 11, 2020
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
9
Evaluating $\int _0^1\frac{\ln ^2\left(x^2+1\right)}{x+1}\:dx$ using real methods
Mar 20, 2020
8
How to evaluate $\sum _{n=1}^{\infty }\left(\frac{H_n^2+H_n^{\left(2\right)}}{n}\right)^2$ in a particular way.
Dec 9, 2020
7
Evaluate $\int _0^{\frac{\pi }{2}}x\cot x\ln ^2(\cos x)\:dx$
May 11, 2021
7
How to find the closed form of $\int _0^{\infty }\frac{\ln \left(x^n+1\right)}{x^n+1}\:\mathrm{d}x$
Jul 7, 2020