associated Legendre functions
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1: 14.1 Special Notation
§14.1 Special Notation
… ►The main functions treated in this chapter are the Legendre functions , , , ; Ferrers functions , (also known as the Legendre functions on the cut); associated Legendre functions , , ; conical functions , , , , (also known as Mehler functions). …2: 14.21 Definitions and Basic Properties
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14.21.1
►Standard solutions: the associated Legendre functions
, , , and .
and exist for all values of , , and , except possibly and , which are branch points (or poles) of the functions, in general.
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§14.21(iii) Properties
…3: 14.31 Other Applications
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§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)). … ►4: 14.26 Uniform Asymptotic Expansions
§14.26 Uniform Asymptotic Expansions
…5: 14.29 Generalizations
6: 14.22 Graphics
§14.22 Graphics
… ►7: 14.25 Integral Representations
8: 14.3 Definitions and Hypergeometric Representations
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