Category Theory
Zulip Server
Archive

You're reading the public-facing archive of the Category Theory Zulip server.
To join the server you need an invite. Anybody can get an invite by contacting Matteo Capucci at name dot surname at gmail dot com.
For all things related to this archive refer to the same person.

Stream: learning: questions

Topic: Bessel functions

Jan Pax (May 28 2025 at 10:10):

In $\frac{d^2u}{dr^2}+\frac{1}{r}\frac{du}{dr}+(\frac{\alpha^2}{c^2}-\frac{n^2}{r^2})u=0$

how it follows $\frac{d^2u}{d\xi^2}+\frac{1}{\xi}\frac{du}{d\xi}+(1-\frac{n^2}{\xi^2})u=0$

where $\xi=\alpha r/c$

?

EDIT

I do not know how to use the chain rule here:

$u(r)=v(\xi)$

$\frac{du}{dr}=\frac{dv}{d\xi}\frac{d\xi}{dr}$

Nathanael Arkor (May 28 2025 at 11:30):

This stream is about questions in category theory. For questions in unrelated areas of mathematics, Math.SE would be more appropriate.

Jan Pax (May 28 2025 at 17:23):

This question there has been closed. No question is dumb here so I dare to ask it here.

Nathanael Arkor (May 28 2025 at 18:04):

No question is dumb, but not every question is relevant to a category theory community. Why was the question closed?

Jan Pax (May 28 2025 at 18:10):

I haven't provided enough effort about what I had tried. Even then, when I did, the question was closed. Here the public is more friendly.Is there a channel here for which this question would be appropriate?

David Corfield (May 28 2025 at 18:31):

Isn't it just:
$\frac{du}{dr}=\frac{du}{d\xi}\frac{d\xi}{dr}= \frac{du}{d\xi}\frac{\alpha}{c}$,
so
$\frac{d^2u}{dr^2}= \frac{d^2u}{d\xi^2}\frac{\alpha^2}{c^2}$.

Madeleine Birchfield (May 28 2025 at 18:56):

People have asked questions about non-category theory related topics here in the past. The difference is that the things they are asking about are usually about research-level mathematics, stuff like rig theory, convergence spaces in topology, constructive real analysis, etc.

But this question is just basic calculus.