The (associated) Legendre function of the first kind P_n^m(z) is the solution to the Legendre differential equation which is regular at the origin. For m, n integers and z real, the Legendre function of the first kind simplifies to a polynomial, called the Legendre polynomial. The associated Legendre function of first kind is given by the Wolfram Language command LegendreP[n, m, z], and the unassociated function by LegendreP[n, z].

associated Legendre polynomial | Legendre differential equation | Legendre function of the second kind | Legendre polynomial