associated_legendre_p Function

public function associated_legendre_p(l, m, x) result(p)

Function to compute the associated Legendre function of x with order l & m ref) Numerical Recipes in Fortran, pp 246-248 $$( l-m ) P^m_l(x) = x ( 2l-1 ) P^m_{l-1}(x) - ( l+m-1 ) P^m_{l-2}(x)$$ $$P^m_m(x) = (-1)^m (2m-1)!! (1-x^2)^(m/2)$$ $$( n!! = 1 \cdot 3 \cdot 5 \cdot ... \cdot m \; \text{where}\; m <= n )$$ $$P^m_{m+1}(x) = x ( 2m+1 ) P^m_m(x)$$

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Arguments

Type	Intent	Optional	Attributes		Name
integer,	intent(in)			::	l
integer,	intent(in)			::	m
real(kind=long),	intent(in)			::	x

Return Value real(kind=long)