• ← LaguerreL
• → LegendreQ

LegendreP

Lengendre polynomials (SymPy, WMA)

LegendreP[n, x]

returns the Legendre polynomial $P_n(x)$.

LegendreP[n, m, x]

returns the associated Legendre polynomial $P^m_n(x)$.

• • LegendreP[4, x]

• • LegendreP[5/2, 1.5]

• • LegendreP[1.75, 1.4, 0.53]

• • LegendreP[1.6, 3.1, 1.5]

LegendreP can be used to draw generalized Lissajous figures:

• • ParametricPlot[ {LegendreP[7, x], LegendreP[5, x]}, {x, -1, 1}]