LegendreQ

LegendreQ[n,z]

gives the Legendre function of the second kind .

LegendreQ[n,m,z]

gives the associated Legendre function of the second kind .

Details

  • 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.

Examples

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Basic Examples  (2)

Compute the 5^(th) Legendre function of the second kind:

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Plot:

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Scope  (7)

Generalizations & Extensions  (3)

Applications  (2)

Properties & Relations  (4)

See Also

LegendreP  SpheroidalQS

Tutorials

Introduced in 1988
(1.0)
| Updated in 1996
(3.0)