A generalized formula for the integral of three associated legendre polynomials

H. A. Mavromatis; R. S. Alassar

doi:10.1016/S0893-9659(98)00180-3

A generalized formula for the integral of three associated legendre polynomials

H. A. Mavromatis^*, R. S. Alassar

^*Corresponding author for this work

Department of Mathematics

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

25 Scopus citations

Abstract

In this paper, a generalized formula for the definite integral of three associated Legendre polynomials of the first kind that arises in various physical applications is given in terms of the ₃F₂ hypergeometric function and the 3 - j symbols. The special case, when the integral reduces to a particularly simple familiar expression, is also mentioned.

Original language	English
Pages (from-to)	101-105
Number of pages	5
Journal	Applied Mathematics Letters
Volume	12
Issue number	3
DOIs	https://doi.org/10.1016/S0893-9659(98)00180-3
State	Published - May 1999

Bibliographical note

Funding Information:
where Re is the Reynolds number. If finite differences are used to solve these equations, many difficulties arise. These include avoiding the indeterminate parts of the equations at the boundaries, and handling the nonlinear part for which central differences result in diagonally nondominant *Author to whom all correspondence should be addressed. The authors wish to acknowledge the support of King Fahd University of Petroleum and Minerals.

ASJC Scopus subject areas

Applied Mathematics

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title = "A generalized formula for the integral of three associated legendre polynomials",

abstract = "In this paper, a generalized formula for the definite integral of three associated Legendre polynomials of the first kind that arises in various physical applications is given in terms of the 3F2 hypergeometric function and the 3 - j symbols. The special case, when the integral reduces to a particularly simple familiar expression, is also mentioned.",

author = "Mavromatis, \{H. A.\} and Alassar, \{R. S.\}",

note = "Funding Information: where Re is the Reynolds number. If finite differences are used to solve these equations, many difficulties arise. These include avoiding the indeterminate parts of the equations at the boundaries, and handling the nonlinear part for which central differences result in diagonally nondominant *Author to whom all correspondence should be addressed. The authors wish to acknowledge the support of King Fahd University of Petroleum and Minerals.",

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AU - Alassar, R. S.

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PY - 1999/5

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N2 - In this paper, a generalized formula for the definite integral of three associated Legendre polynomials of the first kind that arises in various physical applications is given in terms of the 3F2 hypergeometric function and the 3 - j symbols. The special case, when the integral reduces to a particularly simple familiar expression, is also mentioned.

AB - In this paper, a generalized formula for the definite integral of three associated Legendre polynomials of the first kind that arises in various physical applications is given in terms of the 3F2 hypergeometric function and the 3 - j symbols. The special case, when the integral reduces to a particularly simple familiar expression, is also mentioned.

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DO - 10.1016/S0893-9659(98)00180-3

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EP - 105

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

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ER -

A generalized formula for the integral of three associated legendre polynomials

Abstract

Bibliographical note

ASJC Scopus subject areas

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