Integral Representations of Legendre Functions Arising in Poisson Transform

Mathematics. Physics. Mechanics


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. ,



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.


Legendre functions, group representations, Lorentz group, Poisson transform

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