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LegendreQ

LegendreQ[n, z]
gives the Legendre function of the second kind Q_n(z).
LegendreQ[n, m, z]
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 (1-z^2)y^(′′)-2z​y^′+[n(n+1)-m^2/(1-z^2)]y=0.
  • 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.
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