Abstract
In this paper we develop a new method for obtaining Bergman operators with closed-form kernels for equations in two variables. This method results from a combination of the theory of operators of class ∊ and of operators with rational kernels with Laplace's so-called cascade method. Our method yields an extended class of equations that includes members for which no closed-form kernels were known previously, and it also leads to new kmds of closed-form kernels for equations for which so far only class ε operators or operators as developed in [10] were known.
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