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Mathematics
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Nemo
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32
Proof $\int_{-\infty}^\infty\frac{dx}{\left(e^x+e^{-x}+e^{ix\sqrt{3}}\right)^2}=\frac{1}{3}$
Nov 25, 2016
27
Strange symmetry regarding sum $\sum_{n=0}^\infty\frac{n^ne^{-bn}}{\Gamma(n+1)}$ and integral $\int_{0}^\infty\frac{x^xe^{-bx}}{\Gamma(x+1)}dx$
Oct 18, 2017
26
Question about finite analog of $\int_0^\infty \frac{\sin x\sinh x}{\cos (2 x)+\cosh \left(2x \right)}\frac{dx}{x}=\frac{\pi}{8}$
Mar 26, 2020
23
Alternative and more direct proof that an integral is independent of a parameter
Aug 29, 2021
22
Calculate $\int_{0}^\infty\frac{dx}{\left(1+\frac{x^3}{1^3}\right)\left(1+\frac{x^3}{2^3}\right)\left(1+\frac{x^3}{3^3}\right)\ldots}$
Nov 27, 2016
19
Calculate using residues $\int_0^\infty\int_0^\infty{\cos\frac{\pi}2(nx^2-\frac{y^2}n)\cos\pi xy\over\cosh\pi x\cosh\pi y}dxdy,n\in\mathbb{N}$
Jan 19, 2017
19
Prove $\int_0^\infty\Big|\Gamma\Big(\frac13+\frac{i\alpha}{\pi}\Big)\Big|^6\alpha \sinh\alpha~d\alpha=\frac{\pi\sqrt{27}}{4}\Gamma^9\Big(\frac23\Big)$
Oct 23, 2017
19
Trigonometric integral related to Gieseking's constant
May 24, 2019
18
Conjectured closed form for $\sum_{n=-\infty}^\infty\frac{1}{\cosh\pi n+\frac{1}{\sqrt{2}}}$
Aug 23, 2016
15
Solve functional equation $ h(y)+h^{-1}(y)=2y+y^2 $
Dec 8, 2019
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39
What are fixed points of the Fourier Transform
36
Sum of Gaussian pdfs
31
An analogue of the exponential function by replacing infinite series with improper integral
25
Bernoulli sum meets golden number
24
Is there a transformation or a proof for these integrals?