Integral Representations of Legendre Functions Arising in Poisson Transform

Mathematics. Physics. Mechanics


Аuthors

Shilin I. A.1, Vestyak V. A.2*

1. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia
2. ,

*e-mail: kaf311@mai.ru

Abstract

We have derived some integrals representations of Legendre function by using so-called Poisson transform, which maps any homogeneous and infinitely differentiable function on the cone into a corresponding function on the two-sheeted hyperboloid. Above representations are applied in Fourier method or the method of separation of variables in the initial-boundary value problems of Dirichlet and Neumann problem for Poisson equation in a dihedral angle. These problems, in turn, are directly related to the nonlinear flow problem, the lifting force, and vibrations of an airplane wing.

Keywords:

Legendre functions, group representations, Lorentz group, Poisson transform


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