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New generalized Mehler-Fock transformations and applications to the resolvent equation (1809.02757v1)
Published 8 Sep 2018 in math.AP
Abstract: We investigate and solve a special class of integrals involving associated Legendre functions, which can be regarded as generalized Mehler-Fock transformations. Some of the integrals appear naturally when dealing with the heat or resolvent equation of a wedge in the hyperbolic plane. As an application, we derive explicit formulas for the Green's function and the heat kernel of a wedge.