Question

Integral of $e^{-k \cosh(z)} \text {sech}(z) \ dz$ from $z=0$ to $z=\infty$

score 165 · Answer 1 · 2021-04-22 00:52:36

165

Views

Integral of $e^{-k \cosh(z)} \text {sech}(z) \ dz$ from $z=0$ to $z=\infty$

Published on 22 Apr 2021 - 0:52

score 469 · Answer 2 · 2021-04-25 05:01:42

469

Views

Evaluate the series $ \sum_{n=1}^{\infty} \frac{1}{n(e^{2\pi n}-1)} $.

Published on 25 Apr 2021 - 5:01

score 270 · Answer 3 · 2021-04-28 13:48:10

270

Views

If $x=\sinh{\theta}$, is it possible to express $\cosh{n\theta}$ and $\sinh{n\theta}$ in terms of $x$?

Published on 28 Apr 2021 - 13:48

score 118 · Answer 4 · 2021-04-29 08:02:08

118

Views

How can I correctly code the calculation of the Langevin function? [$y=\text{coth}(x)-\frac{1}{x}$]

Published on 29 Apr 2021 - 8:02

score 45 · Answer 5 · 2021-05-05 02:51:11

45

Views

What property must the function $g$ have such that if $\alpha = \beta$ where $g(a)=\alpha$, $g(b)=\beta$, then $a=b$.

Published on 05 May 2021 - 2:51

score 50 · Answer 6 · 2021-05-05 14:52:29

50

Views

Having trouble simplifying a hyperbolic function

Published on 05 May 2021 - 14:52

score 664 · Answer 7 · 2026-03-28 12:49:17

664

Views

Variance of $\tanh z$ where $z\sim{\cal N}(0,\sigma^2)$

Published on 28 Mar 2026 - 12:49

score 235 · Answer 8 · 2021-05-23 11:50:14

235

Views

Verify that $\sinh x\simeq x$?

Published on 23 May 2021 - 11:50

score 66 · Answer 9 · 2021-05-27 07:29:44

66

Views

Generating function of $\coth(n)$

Published on 27 May 2021 - 7:29

score 127 · Answer 10 · 2026-02-23 16:56:52

127

Views

Does the Euler-Mascheroni constant $\gamma$ correspond to infinite hyperbolic angle?

Published on 23 Feb 2026 - 16:56

score 88 · Answer 11 · 2021-06-04 17:57:29

88

Views

Purely geometric proof of inverse hyperbolic trigonometric functions derivatives.

Published on 04 Jun 2021 - 17:57

score 274 · Answer 12 · 2021-06-12 01:36:10

274

Views

Proving $\cosh^2(\cosh x) - \sinh^2 (\sinh x) \geq2$ for real $x$

Published on 12 Jun 2021 - 1:36

score 117 · Answer 13 · 2021-06-13 01:12:25

117

Views

Asymptotic behavior of a Bessel-function-like integral

Published on 13 Jun 2021 - 1:12

score 100 · Answer 14 · 2021-06-20 16:15:06

100

Views

What are the solutions for $\sinh(y)$ $=$ $(-1)^n$ $\sinh(1)$?

Published on 20 Jun 2021 - 16:15

score 30 · Answer 15 · 2021-06-23 13:41:14

30

Views

Basic equivalence of hyperbolic functions expressions

Published on 23 Jun 2021 - 13:41

List Question

Integral of $e^{-k \cosh(z)} \text {sech}(z) \ dz$ from $z=0$ to $z=\infty$

Evaluate the series $ \sum_{n=1}^{\infty} \frac{1}{n(e^{2\pi n}-1)} $.

If $x=\sinh{\theta}$, is it possible to express $\cosh{n\theta}$ and $\sinh{n\theta}$ in terms of $x$?

How can I correctly code the calculation of the Langevin function? [$y=\text{coth}(x)-\frac{1}{x}$]

What property must the function $g$ have such that if $\alpha = \beta$ where $g(a)=\alpha$, $g(b)=\beta$, then $a=b$.

Having trouble simplifying a hyperbolic function

Variance of $\tanh z$ where $z\sim{\cal N}(0,\sigma^2)$

Verify that $\sinh x\simeq x$?

Generating function of $\coth(n)$

Does the Euler-Mascheroni constant $\gamma$ correspond to infinite hyperbolic angle?

Purely geometric proof of inverse hyperbolic trigonometric functions derivatives.

Proving $\cosh^2(\cosh x) - \sinh^2 (\sinh x) \geq2$ for real $x$

Asymptotic behavior of a Bessel-function-like integral

What are the solutions for $\sinh(y)$ $=$ $(-1)^n$ $\sinh(1)$?

Basic equivalence of hyperbolic functions expressions

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