Complex Error Functions as Solutions to Gaussian Integrals

  • #1
I have been told that the following integral can be expressed analytically as a combination of error functions of t. And that the solution can be obtained from then by numerically integrating over t.

[tex]

\int^a_b sin(k_1x)sin(k_2x')\int_0^\infty \frac{1}{\sqrt{t}}e^{-t(x-x')^2}dtdx dx'

[/tex]

While I don't have a problem with numerical integration, I can't see how the expression becomes a combination of error functions. The root t under the line is giving me trouble as well, as it makes the integral look divergent.

Thanks

[edit]-Strictly speaking, this is not course work, as the integral has come up in research. But if that forum is still more appropriate I can move it there.
 

Answers and Replies

  • #2
798
34
First, change t = u²
 

Attachments

  • Gauss Integral.JPG
    Gauss Integral.JPG
    2.7 KB · Views: 324

Related Threads on Complex Error Functions as Solutions to Gaussian Integrals

  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
2
Views
5K
Replies
1
Views
630
Replies
2
Views
2K
  • Last Post
Replies
1
Views
4K
  • Last Post
Replies
3
Views
8K
Replies
2
Views
12K
  • Last Post
Replies
6
Views
3K
Replies
4
Views
970
Top