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# LegendreP

 LegendreP[n, x]gives the Legendre polynomial . LegendreP[n, m, x]gives the associated Legendre polynomial .
• Mathematical function, suitable for both symbolic and numerical manipulation.
• Explicit formulas are given for integers and .
• The Legendre polynomials satisfy the differential equation .
• The Legendre polynomials are orthogonal with unit weight function.
• The associated Legendre polynomials are defined by .
• For arbitrary complex values of n, m and z, LegendreP[n, z] and LegendreP[n, m, z] give Legendre functions of the first kind.
• LegendreP[n, m, a, z] gives Legendre functions of type a. The default is type 1.
• The symbolic form of type 1 involves , of type 2 involves and of type 3 involves .
• Type 1 is defined only for within the unit circle in the complex plane. Type 2 represents an analytic continuation of type 1 outside the unit circle.
• Type 2 functions have branch cuts from to and from to in the complex plane.
• Type 3 functions have a single branch cut from to .
• For certain special arguments, LegendreP automatically evaluates to exact values.
• LegendreP can be evaluated to arbitrary numerical precision.
Compute the 10 Legendre polynomial:
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 Scope   (7)
 Applications   (3)
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