# Finding Roots of Neumann Function N_n(x)

• castusalbuscor
In summary, the student is trying to find the roots of the Neumann function using a function from Wikipedia. The student is not sure how to use the function or how to set up an approximation for it.
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!

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).

Dick said:
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 $$N_{3}$$

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.

Dick said:
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.

## 1. What is the Neumann function Nn(x)?

The Neumann function Nn(x) is a special type of Bessel function that is used to solve differential equations in physics and engineering. It is also known as the modified Bessel function of the second kind.

## 2. How do you find the roots of Neumann function Nn(x)?

The roots of the Neumann function Nn(x) can be found using numerical methods or by using tables or graphs. These methods involve finding the values of x where the function equals zero.

## 3. Why are the roots of the Neumann function Nn(x) important?

The roots of the Neumann function Nn(x) are important because they represent the locations of destructive interference in a wave amplitude. They are also used in the solution of boundary value problems in physics and engineering.

## 4. What is the relationship between the roots of the Neumann function Nn(x) and the Bessel function Jn(x)?

The roots of the Neumann function Nn(x) and the Bessel function Jn(x) are related by the fact that they are both solutions to the same differential equation. In fact, the Neumann function can be expressed as a linear combination of the Bessel function and its derivative.

## 5. Can the roots of the Neumann function Nn(x) be calculated analytically?

No, the roots of the Neumann function Nn(x) cannot be calculated analytically. They can only be approximated using numerical methods or found using tables or graphs. This is due to the complexity of the function and the fact that it does not have a closed-form expression.

• Calculus and Beyond Homework Help
Replies
13
Views
1K
• Calculus and Beyond Homework Help
Replies
8
Views
2K
• Calculus and Beyond Homework Help
Replies
4
Views
1K
• Calculus and Beyond Homework Help
Replies
2
Views
533
• Calculus and Beyond Homework Help
Replies
9
Views
1K
• Calculus and Beyond Homework Help
Replies
3
Views
438
• Calculus and Beyond Homework Help
Replies
14
Views
611
• Calculus and Beyond Homework Help
Replies
8
Views
1K
• Calculus and Beyond Homework Help
Replies
6
Views
1K
• Calculus and Beyond Homework Help
Replies
6
Views
1K