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LegendreP

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description

LegendreP[n, x]
    gives the Legendre polynomial P_n(x).
LegendreP[n, m, x] gives the associated Legendre function P_n^m(x).
LegendreP[n, m, a, x] gives the Legendre function of type a (a in
{1, 2, 3}, default 1). Integer n yields the explicit polynomial; a
non-integer order with an inexact argument evaluates numerically at
machine or arbitrary (MPFR) precision, real or complex. Listable.

Examples

All examples below are verified against the current Mathilda build.

In[1]:= LegendreP[3, x]
Out[1]= -3/2 x + 5/2 x^3

In[2]:= LegendreP[10, 2, x]
Out[2]= (1 - x^2) (3465/128 - 45045/32 x^2 + 675675/64 x^4 - 765765/32 x^6 + 2078505/128 x^8)

Implementation notes

Attributes: Listable, NumericFunction, Protected.

Implementation status

Stable — documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

References