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Legendre Function of the First Kind


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].


See also

Associated Legendre Polynomial, Legendre Differential Equation, Legendre Function of the Second Kind, Legendre Polynomial

Related Wolfram sites

http://functions.wolfram.com/HypergeometricFunctions/LegendrePGeneral/, http://functions.wolfram.com/HypergeometricFunctions/LegendreP2General/, http://functions.wolfram.com/HypergeometricFunctions/LegendreP3General/

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Cite this as:

Weisstein, Eric W. "Legendre Function of the First Kind." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LegendreFunctionoftheFirstKind.html

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