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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

Failed to parse (syntax error): {\displaystyle P_{v}^{u}(x)= \left( {\frac {1+x}{1-x}} \right) ^{1/2\,\mu} {\mbox{$_2$F$_1$}(-v,v+1;\,1-\mu;\,1/2-1/2\,x)} \left( \Gamma \left( 1-\mu \right) \right) ^{-1} }