Lebedev's type index transforms with the squares of the associated Legendre functions
Classical Analysis and ODEs
2017-01-16 v1
Abstract
The classical Lebedev index transform (1967), 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 are proved. As an interesting application, a solution to the boundary value problem for a third order partial differential equation is obtained.
Keywords
Cite
@article{arxiv.1701.03626,
title = {Lebedev's type index transforms with the squares of the associated Legendre functions},
author = {Semyon Yakubovich},
journal= {arXiv preprint arXiv:1701.03626},
year = {2017}
}
Comments
arXiv admin note: text overlap with arXiv:1509.08723