Question

Integrating $\operatorname{arsech}$

score 163 · Answer 1 · 2021-03-29 19:38:06

163

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Integrating $\operatorname{arsech}$

Published on 29 Mar 2021 - 19:38

score 158 · Answer 2 · 2021-03-30 12:15:22

158

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Evaluate $\sum_{n=1}^{\infty} \frac{1}{n^3\sin(\sqrt2n\pi)} $ without using Residue theorem

Published on 30 Mar 2021 - 12:15

score 227 · Answer 3 · 2021-03-30 13:28:40

227

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Second order differential equation with hyperbolic function

Published on 30 Mar 2021 - 13:28

score 752 · Answer 4 · 2021-04-01 08:35:40

752

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Fourier transform of $\operatorname{sech}^2(x)$

Published on 01 Apr 2021 - 8:35

score 47 · Answer 5 · 2026-03-27 03:43:22

47

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Can $x(t) = Acos(at^2+b)$ be interpreted as a generic chaotic trajectory of some dynamical system?

Published on 27 Mar 2026 - 3:43

score 657 · Answer 6 · 2021-04-04 15:36:06

657

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Geodesics in the upper half plane

Published on 04 Apr 2021 - 15:36

score 1.2k · Answer 7 · 2026-03-28 23:57:39

1.2k

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Transformation between different hyperbolic plane coordinate systems

Published on 28 Mar 2026 - 23:57

score 238 · Answer 8 · 2021-04-10 06:18:36

238

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Showing $\sinh z=z\prod_{n=1}^\infty\left(1+\frac{z^2}{n^2\pi^2}\right)$, given $\sin z=z\prod_{n=1}^{ \infty}\left(1 - \frac{z^2}{n^2\pi^2}\right)$

Published on 10 Apr 2021 - 6:18

score 1k · Answer 9 · 2021-04-10 15:46:36

1k

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$\int_0^\infty \log\left(1 - \frac{x}{\sinh x}\right)\,dx$ and generalisations

Published on 10 Apr 2021 - 15:46

score 4.1k · Answer 10 · 2021-04-11 18:15:06

4.1k

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How does the tribonacci sequence have anything to do with hyperbolic functions?

Published on 11 Apr 2021 - 18:15

score 193 · Answer 11 · 2021-04-12 09:44:41

193

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What are the circular-to-hyperbolic trig identities (eg, $\cos(ix)=\cosh(x)$) trying to tell me?

Published on 12 Apr 2021 - 9:44

score 2k · Answer 12 · 2021-04-17 16:57:27

2k

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Fourier transform of piecewise function

Published on 17 Apr 2021 - 16:57

score 65 · Answer 13 · 2021-04-17 18:14:14

Deriving $\cosh \frac{x}{R} = \frac{1}{\sqrt{1- u^2 - v^2}}$ from $x = \frac{R}{2}\;\log\left(\frac{1+\sqrt{u^2 + v^2}}{1-\sqrt{u^2 + v^2}}\right)$

score 123 · Answer 14 · 2021-04-18 08:04:23

123

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How do you integrate $\int x^3\operatorname{sech}^2(x^2)\,\mathrm{d}x\:?$

Published on 18 Apr 2021 - 8:04

score 118 · Answer 15 · 2021-04-20 09:20:32

118

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Ramanujan: $\sqrt{a}\int_0^\infty\frac{e^{-x^2}}{\cosh ax} dx=\sqrt{b}\int_0^\infty\frac{e^{-x^2}}{\cosh bx} dx$, where $ab=\pi$

Published on 20 Apr 2021 - 9:20

List Question

Integrating $\operatorname{arsech}$

Evaluate $\sum_{n=1}^{\infty} \frac{1}{n^3\sin(\sqrt2n\pi)} $ without using Residue theorem

Second order differential equation with hyperbolic function

Fourier transform of $\operatorname{sech}^2(x)$

Can $x(t) = Acos(at^2+b)$ be interpreted as a generic chaotic trajectory of some dynamical system?

Geodesics in the upper half plane

Transformation between different hyperbolic plane coordinate systems

Showing $\sinh z=z\prod_{n=1}^\infty\left(1+\frac{z^2}{n^2\pi^2}\right)$, given $\sin z=z\prod_{n=1}^{ \infty}\left(1 - \frac{z^2}{n^2\pi^2}\right)$

$\int_0^\infty \log\left(1 - \frac{x}{\sinh x}\right)\,dx$ and generalisations

How does the tribonacci sequence have anything to do with hyperbolic functions?

What are the circular-to-hyperbolic trig identities (eg, $\cos(ix)=\cosh(x)$) trying to tell me?

Fourier transform of piecewise function

Deriving $\cosh \frac{x}{R} = \frac{1}{\sqrt{1- u^2 - v^2}}$ from $x = \frac{R}{2}\;\log\left(\frac{1+\sqrt{u^2 + v^2}}{1-\sqrt{u^2 + v^2}}\right)$

How do you integrate $\int x^3\operatorname{sech}^2(x^2)\,\mathrm{d}x\:?$

Ramanujan: $\sqrt{a}\int_0^\infty\frac{e^{-x^2}}{\cosh ax} dx=\sqrt{b}\int_0^\infty\frac{e^{-x^2}}{\cosh bx} dx$, where $ab=\pi$

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