Some results involving generalized associated Legendre functions

In this paper, a new generalization of the associated Legendre functions of the first and the second kinds is introduced using the r-generalized Gauss hypergeometric function. The basic properties of these functions, in particular, some recurrence relations and differential and integral representati...

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Bibliographic Details
Published in:Integral transforms and special functions Vol. 23; no. 2; pp. 105 - 114
Main Authors: Kalla, S. L., Virchenko, N., Lisetska, O.
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 01.02.2012
Taylor & Francis Ltd
Subjects:
Construction
fractional operators
Hypergeometric functions
integral representations
Integrals
Inversions
Legendre functions
Mehler-Fock integral transform
Primary: 33C47
Representations
Secondary: 33C20
Transforms
Whipple formulae
ISSN:1065-2469, 1476-8291
Online Access:Get full text
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Summary:In this paper, a new generalization of the associated Legendre functions of the first and the second kinds is introduced using the r-generalized Gauss hypergeometric function. The basic properties of these functions, in particular, some recurrence relations and differential and integral representations, are given. The Whipple formulae are established. A new generalization of the classical Mehler-Fock integral transform is constructed, and the inversion formula is proved. Some new integrals involving the functions τ, β r P ν μ (t) and are evaluated.
Bibliography:SourceType-Scholarly Journals-1
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ISSN:1065-2469
1476-8291
DOI:10.1080/10652469.2011.564379