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Ferrers function

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Ferrers functions are defined in terms of hypergeometric functions:

Ferrers function of the first kind

$P_{v}^{\mu }(x)=({\frac {1+x}{1-x}})^{\mu /2}*{\frac {F(v+1,-v;1-\mu ;1/2-x/2)}{\Gamma (1-\mu )}}$

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