Integral Representations of Legendre Functions Arising in Poisson Transform
Mathematics. Physics. Mechanics
1. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia
AbstractWe 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