Question

Is it Possible to Evaluate This Limit Without L'Hopital Rule?

score 114 · Answer 1 · 2021-06-25 07:56:28

Is it Possible to Evaluate This Limit Without L'Hopital Rule?

Published on 25 Jun 2021 - 7:56

score 74 · Answer 2 · 2021-06-30 07:00:31

Integrating $I_{\xi}(\rho)=\int^{\infty}_{0}\frac{dt}{t}\frac{\sinh[(\xi+1)t]}{\sinh(\xi t)}\frac{[\cosh(2t)\cos(4\rho t)-1]}{\cosh(t)\sinh(2t)}$

score 136 · Answer 3 · 2021-07-08 02:54:46

136

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Finding $\mathrm{\int_{\Bbb R} a^{cosh(x)} dx}$

Published on 08 Jul 2021 - 2:54

score 255 · Answer 4 · 2026-03-25 16:12:36

255

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On $\mathrm{\sum_{x\in\Bbb Z}sech(x)=3.142242…}$

Published on 25 Mar 2026 - 16:12

score 186 · Answer 5 · 2026-03-28 14:06:35

186

Views

Find the length of the curve $y=\sinh(x)$, $0\leq x\leq1$

Published on 28 Mar 2026 - 14:06

score 1.3k · Answer 6 · 2021-08-03 09:28:09

1.3k

Views

Why is $\frac{7 \cosh(\sqrt 6)}{13}$ near $\pi$?

Published on 03 Aug 2021 - 9:28

score 72 · Answer 7 · 2021-08-06 18:05:47

72

Views

What is the intrinsic equation of the hyperbola?

Published on 06 Aug 2021 - 18:05

score 626 · Answer 8 · 2021-08-07 18:20:38

626

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Compact formula for the $n^\text{th}$ derivative of $\operatorname{sech}^2(x)$?

Published on 07 Aug 2021 - 18:20

score 78 · Answer 9 · 2021-08-19 10:39:15

78

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hyperbolic-function, improper integration and uniform convergence.

Published on 19 Aug 2021 - 10:39

score 97 · Answer 10 · 2021-08-26 16:52:17

97

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An inequality due to Van der Corput

Published on 26 Aug 2021 - 16:52

score 179 · Answer 11 · 2026-03-30 02:24:11

179

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About the inequality $\int_{-\infty}^{0}\left(\cosh\left(x\right)-1\right)^{x}dx<\pi$

Published on 30 Mar 2026 - 2:24

score 229 · Answer 12 · 2021-08-31 17:48:01

229

Views

Is is possible to evaluate $\int \frac{1-\text{sech}(\pi x)}{x} \, dx$ to some reasonable form?

Published on 31 Aug 2021 - 17:48

score 63 · Answer 13 · 2021-09-17 22:27:10

63

Views

Question about hyperbolic angle.

Published on 17 Sep 2021 - 22:27

score 1.1k · Answer 14 · 2021-09-17 23:05:56

1.1k

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How to prove $\int_{0}^{\infty} \frac{(1-x^2) \, \text{sech}^2\left(\frac{\pi x}{2} \right)}{(1+x^2)^2}\, dx = \frac{\zeta(3)}{\pi}$?

Published on 17 Sep 2021 - 23:05

score 139 · Answer 15 · 2021-09-20 10:16:16

139

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In deriving the catenary equation, how does integrating $\frac{dy'}{\sqrt{1+(y')^2}}=\frac1a dx$ yield $\sinh^{-1}(y')=\frac{x}{a}$?

Published on 20 Sep 2021 - 10:16

List Question

Is it Possible to Evaluate This Limit Without L'Hopital Rule?

Integrating $I_{\xi}(\rho)=\int^{\infty}_{0}\frac{dt}{t}\frac{\sinh[(\xi+1)t]}{\sinh(\xi t)}\frac{[\cosh(2t)\cos(4\rho t)-1]}{\cosh(t)\sinh(2t)}$

Finding $\mathrm{\int_{\Bbb R} a^{cosh(x)} dx}$

On $\mathrm{\sum_{x\in\Bbb Z}sech(x)=3.142242…}$

Find the length of the curve $y=\sinh(x)$, $0\leq x\leq1$

Why is $\frac{7 \cosh(\sqrt 6)}{13}$ near $\pi$?

What is the intrinsic equation of the hyperbola?

Compact formula for the $n^\text{th}$ derivative of $\operatorname{sech}^2(x)$?

hyperbolic-function, improper integration and uniform convergence.

An inequality due to Van der Corput

About the inequality $\int_{-\infty}^{0}\left(\cosh\left(x\right)-1\right)^{x}dx<\pi$

Is is possible to evaluate $\int \frac{1-\text{sech}(\pi x)}{x} \, dx$ to some reasonable form?

Question about hyperbolic angle.

How to prove $\int_{0}^{\infty} \frac{(1-x^2) \, \text{sech}^2\left(\frac{\pi x}{2} \right)}{(1+x^2)^2}\, dx = \frac{\zeta(3)}{\pi}$?

In deriving the catenary equation, how does integrating $\frac{dy'}{\sqrt{1+(y')^2}}=\frac1a dx$ yield $\sinh^{-1}(y')=\frac{x}{a}$?

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