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   Articles with "associated legendre" as a keyword



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Lebedev type index transforms with the squares of the associated Legendre functions

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recommendations! 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
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Fractional operators and multi-integral representations for associated Legendre functions

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recommendations! Published in 2022 at "Journal of Mathematical Physics"

DOI: 10.1063/5.0066214

Abstract: In a recent paper, Cohl and Costas-Santos derived a number of interesting multi-derivative and multi-integral relations for the associated Legendre and Ferrers functions in which the orders of those functions are changed in integral steps.… read more here.

Keywords: representations associated; associated legendre; operators multi; multi integral ... See more keywords
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Orthogonality of the Ferrers' associated Legendre functions of the second kind with imaginary argument

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recommendations! 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
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Index transforms with the product of the associated Legendre functions

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recommendations! 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