Title Multi-Integral Representations for Associated Legendre and Ferrers Functions
Authors Cohl, Howard S. , COSTAS SANTOS, ROBERTO SANTIAGO
External publication Si
Means Symmetry
Scope Article
Nature Científica
JCR Quartile 2
SJR Quartile 2
JCR Impact 2.71300
SJR Impact 0.38500
Web https://www.scopus.com/inward/record.uri?eid=2-s2.0-85093703860&doi=10.3390%2fsym12101598&partnerID=40&md5=6dfffdfa62d5552e5753846b33b7c9b9
Publication date 01/10/2020
ISI 000586979700001
Scopus Id 2-s2.0-85093703860
DOI 10.3390/sym12101598
Abstract 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.
Keywords associated legendre functions; ferrers functions; integral representations; gauss hypergeometric function
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