Multi-Integral Representations for Associated Legendre and Ferrers Functions

For the associated Legendre and Ferrers functions of the first and second kind, we obtain new multi-derivative and multi-integral representation formulas. The multi-integral representation formulas that we derive for these functions generalize some classical multi-integration formulas. As a result o...

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Bibliographic Details
Published inSymmetry (Basel) Vol. 12; no. 10; p. 1598
Main Authors Cohl, Howard S., Costas-Santos, Roberto S.
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.10.2020
Subjects
Antisymmetry
associated legendre functions
Derivatives
ferrers functions
gauss hypergeometric function
Harmonic analysis
integral representations
Integrals
Legendre functions
Order parameters
Representations
Theorems
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Summary:For the associated Legendre and Ferrers functions of the first and second kind, we obtain new multi-derivative and multi-integral representation formulas. The multi-integral representation formulas that we derive for these functions generalize some classical multi-integration formulas. As a result of the determination of these formulae, we compute some interesting special values and integral representations for certain particular combinations of the degree and order, including the case where there is symmetry and antisymmetry for the degree and order parameters. As a consequence of our analysis, we obtain some new results for the associated Legendre function of the second kind, including parameter values for which this function is identically zero.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym12101598