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

Chang Yuan Chen; Fa Lin Lu; Dong Sheng Sun; Yuan You; Shi Hai Dong

doi:10.1016/j.aml.2014.10.001

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

Chang Yuan Chen, Fa Lin Lu, Dong Sheng Sun, Yuan You, Shi Hai Dong

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

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.

Original language	English
Pages (from-to)	90-96
Number of pages	7
Journal	Applied Mathematics Letters
Volume	40
DOIs	https://doi.org/10.1016/j.aml.2014.10.001
State	Published - Feb 2015

Keywords

Differential equation
Functional analysis
Universal associated Legendre polynomials

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10.1016/j.aml.2014.10.001

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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",

author = "Chen, {Chang Yuan} and Lu, {Fa Lin} and Sun, {Dong Sheng} and Yuan You and Dong, {Shi Hai}",

year = "2015",

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doi = "10.1016/j.aml.2014.10.001",

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volume = "40",

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journal = "Applied Mathematics Letters",

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T1 - Exact solutions to a class of differential equation and some new mathematical properties for the universal associated-Legendre polynomials

AU - Chen, Chang Yuan

AU - Lu, Fa Lin

AU - Sun, Dong Sheng

AU - You, Yuan

AU - Dong, Shi Hai

PY - 2015/2

Y1 - 2015/2

N2 - 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.

AB - 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.

KW - Differential equation

KW - Functional analysis

KW - Universal associated Legendre polynomials

UR - http://www.scopus.com/inward/record.url?scp=84908398531&partnerID=8YFLogxK

U2 - 10.1016/j.aml.2014.10.001

DO - 10.1016/j.aml.2014.10.001

M3 - Artículo

SN - 0893-9659

VL - 40

SP - 90

EP - 96

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

ER -

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

Abstract

Keywords

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