On a Method for Constructing the Riemann Function for Partial Differential Equations with a Singular Bessel Operator

A linear second-order hyperbolic equation of two independent variables with a singular Bessel operator is considered. For particular types of such equations, a detailed literature review of known methods for constructing Riemann functions is given. It is shown that to construct the Riemann function for equations with a singular Bessel operator, we can use the Erdélyi–Kober transmutation operator. The Riemann function for the Euler–Poisson–Darboux differential equations is found in explicit form. In this paper, we give examples and an algorithm for constructing the Riemann function for second-order hyperbolic equations with the Bessel operator.

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