List questions from hyperbolic-functions

Published on 06 Nov 2020 - 2:06

114

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Prove that $\arctan(\operatorname{arctanh}(x))\geq \operatorname{arctanh}(\arctan(x))$ for $0\leq x <1$

Published on 17 Nov 2020 - 15:21

53

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Are the hyperbolic functions universal for all negative Gaussian curvatures?

Published on 18 Nov 2020 - 16:38

71

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surface of revolution and coordinate change. Does order matter?

Published on 20 Nov 2020 - 0:01

46

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Compute the Maclaurin expansion of $\frac{1 - x \cosh(a)}{1 - 2 \cosh(a) x + x^2}$

Published on 20 Nov 2020 - 18:27

363

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hyperbolic Sine and Cosine Mclaurin series

Published on 20 Nov 2020 - 20:20

130

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$L\{f(x)\}^{-1}=\int^x_a \frac{dx}{f(x)}$

Published on 21 Nov 2020 - 20:40

1k

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Proving that $|\sin(z)|^2 = \sin(x)^2+\sinh(y)^2$

Published on 25 Nov 2020 - 1:38

33

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Prove $\coth\;2v = \frac{x^2 + y^2 + 1}{2y}$

Published on 29 Nov 2020 - 13:44

57

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Prove $\tanh^{-1}\left(\sqrt{\tanh(x)}\right)-\tan^{-1}\left(\sqrt{\tanh(x)}\right)\geq 0$ without using derivative

Published on 01 Dec 2020 - 12:23

62

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Find $\int\cosh^\frac{1}{2}u~du$ and/or $\int\frac{1}{\cosh^\frac{1}{2}\theta}~d\theta$

Published on 29 Mar 2026 - 14:32

110

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Show that the hyperbolic sine function is bijective

Published on 10 Dec 2020 - 0:11

75

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Prove the following and use it to evaluate the integral:

Published on 10 Dec 2020 - 3:47

349

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Integrating $\text{sech}(x)$ using a hyperbolic substitution method

Published on 10 Dec 2020 - 12:15

86

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Conjecture : A lower bound for the prime counting function .

Published on 16 Dec 2020 - 15:23

List Question

How to solve $\frac{1}{\kappa}\tanh^{-1}(\kappa t)+bt=c$ for $t$

Prove that $\arctan(\operatorname{arctanh}(x))\geq \operatorname{arctanh}(\arctan(x))$ for $0\leq x <1$

Are the hyperbolic functions universal for all negative Gaussian curvatures?

surface of revolution and coordinate change. Does order matter?

Compute the Maclaurin expansion of $\frac{1 - x \cosh(a)}{1 - 2 \cosh(a) x + x^2}$

hyperbolic Sine and Cosine Mclaurin series

$L\{f(x)\}^{-1}=\int^x_a \frac{dx}{f(x)}$

Proving that $|\sin(z)|^2 = \sin(x)^2+\sinh(y)^2$

Prove $\coth\;2v = \frac{x^2 + y^2 + 1}{2y}$

Prove $\tanh^{-1}\left(\sqrt{\tanh(x)}\right)-\tan^{-1}\left(\sqrt{\tanh(x)}\right)\geq 0$ without using derivative

Find $\int\cosh^\frac{1}{2}u~du$ and/or $\int\frac{1}{\cosh^\frac{1}{2}\theta}~d\theta$

Show that the hyperbolic sine function is bijective

Prove the following and use it to evaluate the integral:

Integrating $\text{sech}(x)$ using a hyperbolic substitution method

Conjecture : A lower bound for the prime counting function .

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