Legendre equation , the Bessel equation and Sturm Liouville equation

[mano0or]

Show that the Legendre equation as well as the Bessel equation for n=integer are Sturm Liouville equations and thus their solutions are orthogonal. How I can proove that ..?

:(

 

[Jorriss]

Can you put it in sturm-liouville form?

 

[mano0or]

Yes ...

see . this is the form of Sturm Liouville

and this table help me

i found the mathematical explain for bessel .

but i don't know how i can prove their solutions are orthogonal ..!


can you help me

 

[Jorriss]

Did you post the problem exactly? If so, as I interpret it, you do not need to prove that yourself. It is well known that the solutions to sturm-liouville problems are orthogonal and the proof can be found in any mathematical methods book.

 

[mano0or]

yea

i understand that hour before .. i wasn't have enough information about sturm-liouville

or maybe my brain stopped



thanks :)