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].
Legendre Function of the First Kind
See also
Associated Legendre Polynomial, Legendre Differential Equation, Legendre Function of the Second Kind, Legendre PolynomialRelated Wolfram sites
http://functions.wolfram.com/HypergeometricFunctions/LegendrePGeneral/, http://functions.wolfram.com/HypergeometricFunctions/LegendreP2General/, http://functions.wolfram.com/HypergeometricFunctions/LegendreP3General/Explore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Legendre Function of the First Kind." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LegendreFunctionoftheFirstKind.html