Lebedev type index transforms with the squares of the associated Legendre functions
Sign Up to like & getrecommendations! Published in 2017 at "Acta Mathematica Hungarica"
DOI: 10.1007/s10474-017-0748-9
Abstract: The classical Lebedev index transform [3] involving squares and products of the Legendre functions is generalized on the associated Legendre functions of an arbitrary order. Mapping properties are investigated in the Lebesgue spaces. Inversion formulas… read more here.
Keywords: legendre functions; associated legendre; lebedev type; type index ... See more keywords
Orthogonality of the Ferrers' associated Legendre functions of the second kind with imaginary argument
Sign Up to like & getrecommendations! Published in 2017 at "Integral Transforms and Special Functions"
DOI: 10.1080/10652469.2017.1322965
Abstract: ABSTRACT In this work we study the associated Legendre functions of the second kind with a purely imaginary argument . We derive the conditions under which they provide a set of square integrable functions when… read more here.
Keywords: second kind; imaginary argument; legendre functions; functions second ... See more keywords
Index transforms with the product of the associated Legendre functions
Sign Up to like & getrecommendations! Published in 2019 at "Integral Transforms and Special Functions"
DOI: 10.1080/10652469.2019.1611804
Abstract: ABSTRACT Index transforms with the product of the associated Legendre functions are introduced. Mapping properties are investigated in the Lebesgue spaces. Inversion formulas are proved. The results are applied to solve a boundary value problem… read more here.
Keywords: legendre functions; transforms product; associated legendre; product associated ... See more keywords