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I would like to know if is possible to have regular solutions of Legendre equation when the constant $l$ in the Legendre equation $(1-x^2)u''-2xu''+l(l+1)u=0$ is a non integer number?

I am interested in polynomial solutions for non integer.

Thanks in advance!

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    You'll not get polynomials, you'll get the Legendre Functions of the first and second kind.2012-11-03
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    Legendre functions of first kind are polynomials. I think if you have, for example, $l=\frac{\sqrt{13}-1}{2}$ then $l(l+1)=3$ and you will have polynomial solution to Legendre equation for non integer $l$. Is it right?2012-11-03

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