associated Legendre equation
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§14.2(ii) Associated Legendre Equation… ►Ferrers functions and the associated Legendre functions are related to the Legendre functions by the equations , , , , . … ►
§14.2(iii) Numerically Satisfactory Solutions… ►
§14.31(iii) Miscellaneous►Many additional physical applications of Legendre polynomials and associated Legendre functions include solution of the Helmholtz equation, as well as the Laplace equation, in spherical coordinates (Temme (1996b)), quantum mechanics (Edmonds (1974)), and high-frequency scattering by a sphere (Nussenzveig (1965)). …
Previously the exponents of the associated Legendre differential equation (14.2.2) at infinity were given incorrectly by . These were replaced by .
Reported by Hans Volkmer on 2019-01-30
Originally, the factor on the right-hand side was written as , which was taken directly from Watson (1944, p. 412, (13.46.5)), who uses a different normalization for the associated Legendre function of the second kind . Watson’s equals in the DLMF.
Reported by Arun Ravishankar on 2018-10-22
The Wronskian was generalized to include both associated Legendre and Ferrers functions.