Elsevier

Applied Mathematics Letters

Volume 40, February 2015, Pages 90-96
Applied Mathematics Letters

Exact solutions to a class of differential equation and some new mathematical properties for the universal associated-Legendre polynomials

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Abstract

The exact solutions to a class of differential equation are studied. Some special cases are discussed for the central potentials, single ring-shaped potential and the angular Teukolsky equation. A new expression to the associated Legendre polynomials is found. Some new properties of the universal associated-Legendre polynomials (UALPs) including the generating function, Rodrigues’ formula, parity, some special values and the recurrence relations are presented. A new different Rodrigues’ formula of associated Legendre polynomials is also obtained.

Keywords

Differential equation
Functional analysis
Universal associated Legendre polynomials

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