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 thier 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 :)