Some Formulas for Legendre Functions Induced by the Poisson Transform

I. A. Shilin, A. I. Nizhnikov


Using the Poisson transform, which maps any homogeneous and infinitely differentiable function on a cone into a corresponding function on a hyperboloid, we derive some integral representations of the Legendre functions.


Legendre functions; Lorentz group; Poisson transform

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ISSN 1210-2709 (Print)
ISSN 1805-2363 (Online)
Published by the Czech Technical University in Prague