Ferrers function

In mathematics, Ferrers functions are certain special functions defined in terms of hypergeometric functions.^[1] They are named after Norman Macleod Ferrers^{[citation needed]}.

Definitions[]

Ferrers function of the first kind

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

Ferrers function of the second kind

${\displaystyle Q_{v}^{\mu }(x)=\cos(\mu \pi )\left({\frac {1+x}{1-x}}\right)^{\mu /2}{\frac {F(v+1,-v;1-\mu ;1/2-2/x)}{\Gamma (1-\mu )}}}$

See also[]

• Legendre function

References[]