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24
Evaluating integral $\int_0^1 \frac{x-x^2}{\sin \pi x} dx = \frac{7 \zeta(3)}{\pi^3}$
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22
Product $\left(\frac31\right)^{1/2}\cdot\left(\frac75\right)^{1/6}\cdot \left(\frac{11}9\right)^{1/10}\cdot \left(\frac{15}{13}\right)^{1/14}\cdots$
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17
Generalised Integral $I_n=\int_0^{\pi/2} \frac{x^n}{\sin ^n x} \ \mathrm{d}x, \quad n\in \mathbb{Z}^+.$
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14
Prove $\int_0^1 \frac{4\cos^{-1}x}{\sqrt{2x-x^2}}\,dx=\frac{8}{9\sqrt{\pi}}\left(9\Gamma(3/4)^2{}_4F_3(\cdots)+\Gamma(5/4)^2{}_4F_3(\cdots)\right)$
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12
Closed form of $\int_0^\infty \left(\frac{\arctan x}{x}\right)^ndx$
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11
Prove inequality $\arccos \left( \frac{\sin 1-\sin x}{1-x} \right) \leq \sqrt{\frac{1+x+x^2}{3}}$
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9
Prove the following series $\sum\limits_{s=0}^\infty \frac{1}{(sn)!}$
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9
Evaluate $\int_{0}^{\pi }\theta ^{3}\log^{3}\left ( 2\sin\frac{\theta }{2} \right )\mathrm{d}\theta $
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9
To what function does this series converge?
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9
How to prove that $\sum_{k=1}^n\frac{1}{\sqrt[n]{k!} }\sim \frac{n}{\ln n}$
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9
List of integrals or series for Gieseking's constant $\rm{Cl}_2\big(\tfrac{\pi}3\big)$?
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8
Prove that the sum of digits of $(999...9)^{3}$ (cube of integer with $n$ digits $9$) is $18n$
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8
Proof Binomial Coefficient Identity: $\sum_{k=0}^n\frac{k k!}{n^k}\binom{n}{k}=n$
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8
Methods to compute $\sum_{k=1}^nk^p$ without Faulhaber's formula
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7
How can I evaluate the following integral? $\int(\sqrt{x}-x)(e^{\arctan\sqrt{x}})^2dx$
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7
Evaluating $\lim\limits_{n\to\infty} e^{-n} \sum\limits_{k=0}^{n} \frac{n^k}{k!}$
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7
Is $\zeta(s)\sim\sqrt{\frac{\zeta(4s)}{\zeta(2s)}}\prod\limits_{n=1}^\infty\big(1-\frac{2}{p_n^s+p_n^{-s}}\big)^{-1/2}$?
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7
general formula for the nth derivative of $f(x)=\frac{1}{1+e^{x}}$
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6
Prove that $\ln{\left({A^6\sqrt{\pi}\over 2^{7\over6}e}\right)}=\sum\limits_{n=1}^{\infty}{(-1)^{n+1}\over n(n+1)}\eta(n)$
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6
Q: How does one show that $\int_{0}^{1}{1-x^{\sqrt5}\over (1-x^{\phi})^{\phi}}\mathrm dx={\phi^2}?$
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6
Complex Integration - $\int_{-\infty}^{\infty} \frac{x-1}{x^5-1} dx$
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6
An integral of a rational function of logarithm and nonlinear arguments
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6
Prove that ${e\over {\pi}}\lt{\sqrt3\over{2}}$ without using a calculator.
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6
Evaluation of :$\sum_{n=1}^{\infty}\frac{\sin n \log n}{n}$
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6
Trying to solve $\int_{0}^{\infty}\frac{\operatorname{arccot}\left(\sqrt{1+x}+\sqrt{2+x}\right)}{1+x} dx$
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6
Mathematical Explanation of Mathematica Summation ${\sum_{n=1}^{\infty}\frac{(2n-1)!}{(2n+2)!}\zeta(2n)}$
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6
Proving that $\sum_{k=0}^{n}\frac{(-1)^k}{{n\choose k}}=[1+(-1)^n] \frac{n+1}{n+2}.$
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5
How to solve differential equation $(y'/y)'=a((b/x^2)+xy)$?
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5
Evaluate $\int\limits_0^1\frac{\log(1-x+x^2)\log(1+x-x^2)}{x}dx$
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5
Elementary summations of non-elementary functions
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