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...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:Integral transforms and special functions Ročník 23; číslo 2; s. 105 - 114
Hlavní autoři: Kalla, S. L., Virchenko, N., Lisetska, O.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Abingdon Taylor & Francis 01.02.2012
Taylor & Francis Ltd
Témata:
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
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Popis
Shrnutí: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.
Bibliografie:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ObjectType-Article-2
content type line 23
ISSN:1065-2469
1476-8291
DOI:10.1080/10652469.2011.564379