gives the Legendre function of the second kind .

gives 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[n,m,a,z] 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.
  • LegendreQ automatically threads over lists.
Introduced in 1988
| Updated in 1996