How do you combine Bessel functions?

  • Thread starter renz
  • Start date
  • #1
renz
28
0
Hi,
I have been trying to solve this differential equation for a while now. Now I get to the point where I have the solution, but it includes an integral.

The integral is

[tex]\int x J_{1/4}(ax) J_{1/4}(bx) e^{-x^2t}dx[/tex]

, where a and b are constants, and the integral is from zero to infinity. I think I can figure out how to integrate this by using a table of integral, but I need to only have one Bessel function in it.
How can I combine the two Bessel functions?

Any help is much appreciated.
 

Answers and Replies

  • #2
IttyBittyBit
160
0
What do you mean by 'need to have one Bessel function in it?' If you mean the antiderivative, well I believe the antiderivative has no closed form. The problem is the e^(-t*x^2) in there.

Why don't you post the original DE?
 
  • #3
renz
28
0
thank you for replying. I thought there's a way to make the product of two Bessel function become one function, or square of one function.

But never mind, I found the solution to the integral.
 

Suggested for: How do you combine Bessel functions?

  • Last Post
Replies
2
Views
153
  • Last Post
Replies
3
Views
243
Replies
5
Views
586
  • Last Post
Replies
2
Views
503
Replies
1
Views
1K
  • Last Post
Replies
4
Views
902
Replies
9
Views
257
Replies
2
Views
1K
  • Last Post
Replies
1
Views
8K
Top