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My question concerns the associated or generalized Legendre polynomials. They are labeled by two numbers $m$ and $l$; i.e., $P_l^m(x)$, for $x \in [-1,1]$. Usually one assumes that $m$ and $l$ are both integers, but I suspect that it is possible for them to be half integers. If this is correct, what is the meaning of formulas like

$$P_l^{-m}(x)=(-1)^m \frac{(l-m)!}{(l+m)!}P_l^m(x)$$

or Rodrigues's formula?

Thanks

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    Can you link a reference in which these polynomial are used?2012-01-25
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    The most similar thing I am able to find is this paper Hunter et al. "Fermion quasi-spherical harmonics" J. Phys. A: Math. Gen. 32 795 (1999).2012-01-25

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