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Legendre equation , the Bessel equation and Sturm Liouville equation

by mano0or
Tags: bessel, equation, legendre, liouville, sturm
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mano0or
#1
Dec28-12, 08:35 AM
P: 3

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 ..?

:(
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Jorriss
#2
Dec28-12, 11:28 AM
P: 1,042
Can you put it in sturm-liouville form?
mano0or
#3
Dec28-12, 12:41 PM
P: 3
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
#4
Dec28-12, 03:14 PM
P: 1,042
Legendre equation , the Bessel equation and Sturm Liouville equation

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
#5
Dec28-12, 03:27 PM
P: 3
yea

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

or maybe my brain stopped



thanks :)


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