Show that the Hermite polynomials H2(x) and H3(x).

  • Thread starter ASIWYFA
  • Start date
  • #1
3
0
Hi guys. Im new, and i need help badly. I have been asked this question and I have no idea how to do it. Any help would be appreciated!



Show that the Hermite polynomials H2(x) and H3(x) are orthogonal on
x € [-L, L], where L > 0 is a constant,
H2(x) = 4x² - 2 and H3(x) = 8x³ - 12x

Thanks in advance.
 

Answers and Replies

  • #2
22,129
3,297
You need to show that

[tex]\int_{-L}^L{(4x^2-2)(8x^3-12x)dx}=0[/tex]

This seems an easy integral...

Or do you consider another inner product??
 
  • #3
3
0
Yes you are correct. THanks you. I believe I have solved the problem correctly.
 
  • #4
uart
Science Advisor
2,784
12
One thing that's worth pointing out about this problem is that while there are other ways for functions to be orthogonal over a specific interval (like [-1,1] for example), the only way possible for functions to be orthogonal over the arbitrary interval [-L,L] is if their product is an odd function.

So the original question is equivalent to showing that the product of H2 and H3 is an odd function.
 

Related Threads on Show that the Hermite polynomials H2(x) and H3(x).

Replies
4
Views
2K
  • Last Post
Replies
7
Views
4K
Replies
1
Views
1K
  • Last Post
Replies
4
Views
2K
Replies
16
Views
3K
Replies
2
Views
1K
Replies
7
Views
2K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
1
Views
900
  • Last Post
Replies
2
Views
2K
Top