# Questions tagged [envelope]

In geometry, an Envelope of a family of curves is a curve that touches each member of that family at same family. Therefore it is the limiting curve of intersection of contiguous members the initial family.

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### What differential equations describe absolute squares of Hankel-like functions of real numbers?

The linearly independent solutions of Bessel equation can be combined into two complex functions, which would represent running radial cylindrical waves. These are the Hankel functions $H_\alpha^{(1)}$...
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### Envelopes In Mathematics

How can I make sure that when we eliminate the parameter from the curve \begin{align*} F(t,x,y) &= 0 \\ \frac{\partial F}{\partial t}(t,x,y) &= 0\,, \end{align*} the equation obtained is the ...
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### How is this integral computed??

I'm reading this book about electrical properties of materials where the electron is introduced as a wave. Using the equation of a wave, they bring about the "envelope" of a wave. So here is how the ...
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### Envelope of a family of data plots

I have a transfer function $$M(s;\theta)=\frac{K(\theta) s (s+z(\theta))}{(s^2+2\xi\omega_n s+w_n^2)^2}$$ where $K$ and $z$ are constants that depend on some parameters $\theta$. I plotted the step ...
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