Constructing the Riemann–Hadamard Function for a Fourth-Order Bianchi Equation

The Darboux problem and the definition of the Riemann–Hadamard function are presented for the Bianchi equation of the fourth order—a linear fourth-order equation with four independent variables that has a dominant derivative not containing multiple differentiation with respect to any of the independent variables. Sufficient conditions on the coefficients of this equation under which its Riemann–Hadamard function allows explicit construction in terms of hypergeometric functions are obtained.