Construction of the Riemann–Hadamard function for the three-dimensional Bianchi equation

For a third-order equation with a dominant partial derivative (the Bianchi equation), the statement of the Darboux problem and the definition of the Riemann–Hadamard function are given. Based on the possibility of representing the Riemann function explicitly for a class of third-order Bianchi equations equivalent in function, sufficient conditions are proposed for the coefficients of the Bianchi equation that provide construction of the Riemann–Hadamard function in terms of hypergeometric functions.