Question

Conjectured relation between hyperbolic sums

score 101 · Answer 1 · 2023-03-03 10:14:46

101

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Conjectured relation between hyperbolic sums

Published on 03 Mar 2023 - 10:14

score 111 · Answer 2 · 2023-03-06 00:14:51

111

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Calculate the length of the curve $\vec r(t)= a(\sinh t-t)\vec i+a(1-\cosh t)\vec j$ from $t = 0$ to $t = T$?

Published on 06 Mar 2023 - 0:14

score 79 · Answer 3 · 2026-03-26 06:30:55

79

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Can you explain why $du/\sqrt{c-2u} = d\varepsilon$ using hyperbolic substitution integral becomes $A\operatorname{sech}^2(t)$?

Published on 26 Mar 2026 - 6:30

score 73 · Answer 4 · 2023-03-19 11:22:37

73

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Proving $\cosh\alpha = \frac{\cos a}{1-\cos a}$ for a regular hyperbolic triangle with all side-lengths $\alpha$ and all angles $a$

Published on 19 Mar 2023 - 11:22

score 133 · Answer 5 · 2023-03-24 09:56:48

133

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Prove that $\tanh (\cosh^{-1} (x)) = \frac{\sqrt{x^2-1}}{x}$

Published on 24 Mar 2023 - 9:56

score 90 · Answer 6 · 2023-03-25 15:17:35

90

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2D Laplacian with 1 Non-Homogeneous Dirichlet, 1 Homogeneous Dirichlet and 2 Homogeneous Neumann BCs, Rectangular Domain

Published on 25 Mar 2023 - 15:17

score 91 · Answer 7 · 2023-03-27 21:36:23

91

Views

Is there a generalization for the conversion cosh(z)=cos(iz)?

Published on 27 Mar 2023 - 21:36

score 174 · Answer 8 · 2023-03-29 09:29:06

174

Views

Prove or (dis)prove that : $f(x,y)\geq 0$

Published on 29 Mar 2023 - 9:29

score 77 · Answer 9 · 2023-04-03 15:10:52

77

Views

Is there a power series for $\text{sech}(x)$ valid for all $x$? Or for $x>\frac{\pi}{2}$?

Published on 03 Apr 2023 - 15:10

score 214 · Answer 10 · 2023-04-05 06:52:52

214

Views

Show that $\sinh^{-1}(x) = \ln(x + \sqrt{x^2 + 1})$

Published on 05 Apr 2023 - 6:52

score 209 · Answer 11 · 2026-03-27 00:57:12

209

Views

Generalization of $\int_0^{\infty} e^{-x^2} \cosh x d x$?

Published on 27 Mar 2026 - 0:57

score 96 · Answer 12 · 2023-04-20 07:44:59

96

Views

Is the error function essential to $\int_0^{\infty} e^{-a x^2} \sinh (b x) d x$?

Published on 20 Apr 2023 - 7:44

score 1.4k · Answer 13 · 2023-04-21 09:46:48

1.4k

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Can the integral be found without Feynman’s trick?

Published on 21 Apr 2023 - 9:46

score 368 · Answer 14 · 2023-04-28 08:10:34

368

Views

Closed-form Maclaurin series of $\log\cosh(x)$

Published on 28 Apr 2023 - 8:10

score 49 · Answer 15 · 2023-04-28 09:55:18

49

Views

Simplify $\cosh{\pi ny} - \coth{\pi n}\sinh{\pi n y}$

Published on 28 Apr 2023 - 9:55

List Question

Conjectured relation between hyperbolic sums

Calculate the length of the curve $\vec r(t)= a(\sinh t-t)\vec i+a(1-\cosh t)\vec j$ from $t = 0$ to $t = T$?

Can you explain why $du/\sqrt{c-2u} = d\varepsilon$ using hyperbolic substitution integral becomes $A\operatorname{sech}^2(t)$?

Proving $\cosh\alpha = \frac{\cos a}{1-\cos a}$ for a regular hyperbolic triangle with all side-lengths $\alpha$ and all angles $a$

Prove that $\tanh (\cosh^{-1} (x)) = \frac{\sqrt{x^2-1}}{x}$

2D Laplacian with 1 Non-Homogeneous Dirichlet, 1 Homogeneous Dirichlet and 2 Homogeneous Neumann BCs, Rectangular Domain

Is there a generalization for the conversion cosh(z)=cos(iz)?

Prove or (dis)prove that : $f(x,y)\geq 0$

Is there a power series for $\text{sech}(x)$ valid for all $x$? Or for $x>\frac{\pi}{2}$?

Show that $\sinh^{-1}(x) = \ln(x + \sqrt{x^2 + 1})$

Generalization of $\int_0^{\infty} e^{-x^2} \cosh x d x$?

Is the error function essential to $\int_0^{\infty} e^{-a x^2} \sinh (b x) d x$?

Can the integral be found without Feynman’s trick?

Closed-form Maclaurin series of $\log\cosh(x)$

Simplify $\cosh{\pi ny} - \coth{\pi n}\sinh{\pi n y}$

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