Finding Roots of Neumann Function N_n(x)

[castusalbuscor]

So for an assignment I have to write a program to find the roots of the Neumann function $$N_{n}(x)$$. However the only Neumann function I have in my class notes is:

Which is not overly helpful, and its the only one that was "boxed" in class.

Any hints on how I can incorporate that into a computer program to find the roots would be great!

 

[Dick]

What system are you using to write the program? If it's something like Mathematica you should find that the Neumann function is already defined (as a form of Bessel function).

 

[castusalbuscor]

What system are you using to write the program? If it's something like Mathematica you should find that the Neumann function is already defined (as a form of Bessel function).

I've never used Mathematica, though there seems to be a lot of people mentioning it. The prof wants us to use either C/C++ or FORTRAN. I have some experience with C++ so that's what I would be using.
Also I would be compiling it in Unix/Linux, if that helps...

Found an equation on Wikipedia:

$$Y_{\alpha} = \frac{J_{\alpha}cos(\alpha \pi) - J_{- \alpha}}{sin(\alpha \pi)}$$
​

This one seems more promising, but not sure how to use it to find the first five roots for $$N_{1}$$, $$N_{2}$$, and $$N_{3}$$

 

[Dick]

You should find built in functions in the C math libraries, things like jn and yn. Setting up decent approximations for transcendental functions like this is a job for a numerical analysis type person. Just finding roots once the functions are defined isn't so hard.

 

[castusalbuscor]

You should find built in functions in the C math libraries, things like jn and yn. Setting up decent approximations for transcendental functions like this is a job for a numerical analysis type person. Just finding roots once the functions are defined isn't so hard.

Sounds doable.. will. report back with success or failure.