Legendre Polynomial solutions

1. May 19, 2005

h.a.y.l.e.y

Hi,
I have a problem where I am given the Legendre equation and have been told 1 solution is u(x). It asks me to obtain an expression for the second solution v(x) corresponding to the same value of l.
I think it requires Sturm Liouville treatment but don't have a clue how to begin.
Please HELP!

2. May 19, 2005

dextercioby

3. May 19, 2005

HallsofIvy

Staff Emeritus
More generally, if you have a known solution, u(x) to a differential equation, Taking
y(x)= u(x)v(x), where v(x) is an unknown function, and plugging into the equation,you get an equation of order one lower for v. In particular, if you know one solution to a second order equation, this will give you a first order equation for an independent solution v(x).

4. May 19, 2005

h.a.y.l.e.y

OK so I've skimmed that page and its confirmed what I've got in my lecture notes (albeit in a more complex manner!) :surprised
The question remains though, how would I be expected to answer the question, given that this question is only worth 9 marks out of a possible 25 on my exam sheet?!
Surely its asking for something a lot more direct, and I'm still in the dark as to how to begin and what to do.........

5. May 19, 2005

dextercioby

Take Halls' advice and do what he said.I'm sure u'll get the second indep.solution.

Daniel.

6. May 19, 2005

h.a.y.l.e.y

Yes, sorry I was typing that reply whilst Hall's was posted.
Thanks for your help, I think I know where to go from here
x

7. Feb 8, 2010

tulips

Can somebody help me in deriving legendre differential function using its generating function

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