Function defined by P ℓ ( m ) ( x ) = ( 1 − x 2 ) m / 2 d m d x m P ℓ ( x ) {\displaystyle P_{\ell }^{(m)}(x)=(1-x^{2})^{m/2}{\tfrac {d^{m}}{dx^{m}}}P_{\ell }(x)} where Pℓ denotes a Legendre function.
