This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
 BUILT-IN MATHEMATICA SYMBOL

# LegendreQ

 LegendreQgives the Legendre function of the second kind . LegendreQgives the associated Legendre function of the second kind .
• Mathematical function, suitable for both symbolic and numerical manipulation.
• For integers n and m, explicit formulas are generated.
• The Legendre functions satisfy the differential equation .
• LegendreQ gives Legendre functions of type a. The default is type 1.
• LegendreQ of types 1, 2, and 3 are defined in terms of LegendreP of these types, and have the same branch cut structure.
• For certain special arguments, LegendreQ automatically evaluates to exact values.
• LegendreQ can be evaluated to arbitrary numerical precision.
Compute the 5 Legendre function of the second kind:
Plot:
Compute the 5 Legendre function of the second kind:
 Out[1]=

Plot:
 Out[1]=
 Scope   (7)
Compute the associated Legendre function of the second kind:
Evaluate for fractional orders:
Evaluate for complex arguments:
Evaluate to high precision:
The precision of the output tracks the precision of the input: