Question

Prove that $\sum_{n\geq 1} \frac{1}{x+n^2}=\frac{\pi\sqrt{x}\operatorname{coth}(\pi\sqrt{x})-1}{2x}$ for all $x>0$

score 754 · Answer 1 · 2018-05-15 20:17:24

754

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Prove that $\sum_{n\geq 1} \frac{1}{x+n^2}=\frac{\pi\sqrt{x}\operatorname{coth}(\pi\sqrt{x})-1}{2x}$ for all $x>0$

Published on 15 May 2018 - 20:17

score 60 · Answer 2 · 2018-05-16 09:15:08

60

Views

Closed Form of the following infinite series

Published on 16 May 2018 - 9:15

score 408 · Answer 3 · 2018-05-22 05:28:36

408

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Evaluate $\int_{0}^{\infty} \frac{x \exp\left\{-\beta^2 x^2\right\}}{\sinh \left(\frac{\pi x}{2}\right)} \mathrm{d} x$

Published on 22 May 2018 - 5:28

score 112 · Answer 4 · 2018-05-25 03:58:22

112

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Series Expansion of $\int_{\mathbb{R}} \tanh\left(\beta x\right) x \exp\left(-\frac{x^2}{2}\right) \mathrm{d} x$

Published on 25 May 2018 - 3:58

score 179 · Answer 5 · 2018-05-26 21:00:22

179

Views

Geometric method to calculate $\tanh(\cosh^{-1}(x))$

Published on 26 May 2018 - 21:00

score 1.3k · Answer 6 · 2018-05-31 14:11:45

1.3k

Views

What are Hyperbolic Trig Functions Functions of?

Published on 31 May 2018 - 14:11

score 1.6k · Answer 7 · 2018-06-05 12:06:09

1.6k

Views

Fitting hyperbolic functions ($\tanh$) on data.

Published on 05 Jun 2018 - 12:06

score 852 · Answer 8 · 2018-06-09 19:19:12

852

Views

Hyperbolic inverse Function

Published on 09 Jun 2018 - 19:19

score 1.2k · Answer 9 · 2018-06-10 06:59:11

1.2k

Views

Find $\lim_{x\to 0} \frac{\sinh x -\sin x}{\cosh x - \cos x}$

Published on 10 Jun 2018 - 6:59

score 2.3k · Answer 10 · 2018-06-11 12:43:32

2.3k

Views

Solving hyperbolic functions

Published on 11 Jun 2018 - 12:43

score 407 · Answer 11 · 2018-06-12 17:22:18

407

Views

Hyperbolic tangent expansion in temperature

Published on 12 Jun 2018 - 17:22

score 220 · Answer 12 · 2018-06-17 14:14:14

220

Views

Proving that $\cosh(x)\cosh(y) \geq \sqrt{x^2 + y^2}$

Published on 17 Jun 2018 - 14:14

score 430 · Answer 13 · 2018-06-17 17:53:36

430

Views

Proving that $\cosh^{-1} (\cosh(x)\cosh(y) ) \geq \sqrt{x^2 + y^2}$ and the CAT(0) inequality

Published on 17 Jun 2018 - 17:53

score 515 · Answer 14 · 2018-06-25 22:24:41

515

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What is the period of the composition of hyperbolic tangent and hyperbolic arcsine?

Published on 25 Jun 2018 - 22:24

score 5k · Answer 15 · 2018-06-27 06:48:22

5k

Views

Infinite Product Expansion of Hyperbolic Functions

Published on 27 Jun 2018 - 6:48

List Question

Prove that $\sum_{n\geq 1} \frac{1}{x+n^2}=\frac{\pi\sqrt{x}\operatorname{coth}(\pi\sqrt{x})-1}{2x}$ for all $x>0$

Closed Form of the following infinite series

Evaluate $\int_{0}^{\infty} \frac{x \exp\left\{-\beta^2 x^2\right\}}{\sinh \left(\frac{\pi x}{2}\right)} \mathrm{d} x$

Series Expansion of $\int_{\mathbb{R}} \tanh\left(\beta x\right) x \exp\left(-\frac{x^2}{2}\right) \mathrm{d} x$

Geometric method to calculate $\tanh(\cosh^{-1}(x))$

What are Hyperbolic Trig Functions Functions of?

Fitting hyperbolic functions ($\tanh$) on data.

Hyperbolic inverse Function

Find $\lim_{x\to 0} \frac{\sinh x -\sin x}{\cosh x - \cos x}$

Solving hyperbolic functions

Hyperbolic tangent expansion in temperature

Proving that $\cosh(x)\cosh(y) \geq \sqrt{x^2 + y^2}$

Proving that $\cosh^{-1} (\cosh(x)\cosh(y) ) \geq \sqrt{x^2 + y^2}$ and the CAT(0) inequality

What is the period of the composition of hyperbolic tangent and hyperbolic arcsine?

Infinite Product Expansion of Hyperbolic Functions

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