Legendre Function of the First Kind

The (associated) Legendre function of the first kind  is the solution to the Legendre differential equation which is regular at the origin. For  integers and  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].