New generalized Mehler-Fock transformations and applications to the resolvent equation

Eren Ucar

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arXiv · 1809.02757

New generalized Mehler-Fock transformations and applications to the resolvent equation

Eren Ucar

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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.

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Eren Ucar. 2018-09-08. New generalized Mehler-Fock transformations and applications to the resolvent equation. https://arxiv.org/abs/1809.02757

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