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New posts in hyperbolic-functions
Series $\sum\limits_{n=1}^\infty \frac{1}{\cosh(\pi n)}= \frac{1}{2} \left(\frac{\sqrt{\pi}}{\Gamma^2 \left( \frac{3}{4}\right)}-1\right)$
sequences-and-series
analysis
hyperbolic-functions
Need help with $\int_0^1\frac{\log(1+x)-\log(1-x)}{\left(1+\log^2x\right)x}\,dx$
calculus
integration
definite-integrals
hyperbolic-functions
Use residues to evaluate $\int_0^\infty \frac{\cosh(ax)}{\cosh(x)}\,\mathrm{d}x$, where $|a|<1$
residue-calculus
hyperbolic-functions
Why is $\frac{7 \cosh(\sqrt 6)}{13}$ near $\pi$?
calculus
approximation
pi
hyperbolic-functions
Prove $\int_0^1 \frac{\tanh^{-1} (\beta t) dt}{t\sqrt{(1-t)(1- \alpha t)}}=\log (a) \log (b)$
integration
definite-integrals
logarithms
hyperbolic-functions
$\int_0^\infty(\log x)^2(\mathrm{sech}\,x)^2\mathrm dx$
improper-integrals
closed-form
hyperbolic-functions
Is $1 / \sinh (4x)$ equal to $\operatorname{csch} (4x)$?
trigonometry
hyperbolic-functions
A tricky integral involving hyperbolic functions
calculus
integration
hyperbolic-functions
Why are the domain and image of $F(x) = \sqrt{1-\cosh(x)}$ only $\{0\}$? [closed]
algebra-precalculus
functions
graphing-functions
hyperbolic-functions
Is hyperbolic rotation really a rotation?
linear-transformations
transformation
hyperbolic-geometry
hyperbolic-functions
How were hyperbolic functions derived/discovered?
trigonometry
math-history
hyperbolic-functions
Closed-form of $\int_0^\infty \frac{1}{\left(a+\cosh x\right)^{1/n}} \, dx$ for $a=0,1$
calculus
integration
definite-integrals
closed-form
hyperbolic-functions
What is the importance of $\sinh(x)$?
calculus
hyperbolic-functions
Unifying the connections between the trigonometric and hyperbolic functions
calculus
trigonometry
exponential-function
hyperbolic-functions
Evaluate the series $ \sum_{n=1}^{\infty} \frac{1}{n(e^{2\pi n}-1)} $.
sequences-and-series
hyperbolic-functions
Can hyperbolic functions be defined in terms of trigonometric functions?
trigonometry
exponential-function
hyperbolic-functions
Closed form for $\int_{-\infty}^\infty\operatorname{sech}(x)\operatorname{sech}(a\, x)\ dx$
calculus
integration
definite-integrals
closed-form
hyperbolic-functions
Is there an inequality for $\sinh(x)$ which is similar to this inequality $\cosh(x)\leq e^{x^2/2}$
trigonometry
inequality
hyperbolic-functions
Curious about an empirically found continued fraction for tanh
number-theory
closed-form
continued-fractions
hyperbolic-functions
Integral ${\large\int}_0^\infty\frac{dx}{\sqrt[4]{7+\cosh x}}$
calculus
integration
definite-integrals
closed-form
hyperbolic-functions
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