# Questions tagged [hyperbolic-functions]

For questions related to hyperbolic functions: $\sinh$, $\cosh$, $\tanh$, and so on.

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### Is there an exact expression for the full width half maximum of a sech^2 curve convolved on itself?

As some simple math can show, a Gaussian convolved onto itself is also a Gaussian. Importantly, the FWHM of the original gaussian compared to that of its convolved counterpart is different by a factor ...
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### $|\sinh(\Im z)| \leq |\cos z| \leq \cosh(\Im z),$ what estimate do we get if $z \in \mathbb{R}$?

Prove that for every $z \in \mathbb{C}$ the following holds: $$|\sinh(\Im z)| \leq |\cos z| \leq \cosh(\Im z).$$ What estimate do we get if $z \in \mathbb{R}$? Attempt: To prove the given ...
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### Given the function $f$ with the rule $f(z) = \frac{z \sinh\left(\frac{1}{z^2}\right)}{z^2 + 1}$.

Given the function $f$ with the rule $f(z) = \frac{z \sinh\left(\frac{1}{z^2}\right)}{z^2 + 1}$. (a) Determine and classify the singular points of the function $f$ and calculate the residues at these ...
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### Optimal length of rope for sliding across a gap

I'm trying to solve a physics problem that I heard ~10 years ago in undergrad that was casually posed to me without a solution in mind; it has been bothering me ever since! Please let me know if this ...
• 262
1 vote
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### Understanding the Properties and Applications of My Custom Kernel Function

I am a hobbyist and I have made this kernel that I want to use for varies things. Can you please help me understand the proprieties of what I have created and how I can possibly integrate it correctly ...
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### Growth of distance between divergent hyperbolic lines is at least linear in the arc-length parameter

I'm trying to do Chapter 3 Problem 21 in Geometry and Topology (Reid M., Szendroi B.) 2005 ed. The hyperbolic plane ${\cal H}^2=\{(t,x,y):t^2-x^2-y^2=1,t>0\}$ WLOG let $L_1$ be the hyperbolic line ...
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### cvxpy with a tanh objective

I need to solve an optimisation problem of the form: \begin{align} \textrm{maximize} \quad &\sum_{i=1}^{n} a_i \tanh(c_i x_i/2) \\ \textrm{wrt} \quad &x_i, \quad i \in 1,\dots,n \\ \textrm{...
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