Top network posts

• 66 Evaluating the log gamma integral $\int_{0}^{z} \log \Gamma (x) \, \mathrm dx$ in terms of the Hurwitz zeta function
• 62 Prove $\int\limits_{0}^{\pi/2}\frac{dx}{1+\sin^2{(\tan{x})}}=\frac{\pi}{2\sqrt{2}}\bigl(\frac{e^2+3-2\sqrt{2}}{e^2-3+2\sqrt{2}}\bigr)$
• 49 Prove $\int_0^{\infty}\! \frac{\mathbb{d}x}{1+x^n}=\frac{\pi}{n \sin\frac{\pi}{n}}$ using real analysis techniques only
• 43 How to prove that $\frac{\zeta(2) }{2}+\frac{\zeta (4)}{2^3}+\frac{\zeta (6)}{2^5}+\frac{\zeta (8)}{2^7}+\cdots=1$?
• 40 A series involving the harmonic numbers : $\sum_{n=1}^{\infty}\frac{H_n}{n^3}$
• 39 Evaluating the series $\sum\limits_{n=1}^{\infty} \frac{1}{n^{3} \binom{2n}{n}} $
• 35 Integral involving logarithm: $\int_0^\infty \frac{ \ln x}{(x+a)(x+b)} dx$
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