In this paper, we state the Darboux problem and give the definition of the Riemann–Hadamard function for a third-order equation with dominant partial derivative (the Bianchi equation). Basing on the possibility of explicitly representing the Riemann function for a certain class of Bianchi equations of the third order, which are equivalent with respect to function, we establish sufficient conditions for coefficients of the Bianchi equation that provide the construction of the Riemann–Hadamard function in terms of hypergeometric functions.

中文翻译：

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三维Bianchi方程的Riemann-Hadamard函数的构造

在本文中，我们陈述了Darboux问题，并给出了具有优势偏导数的三阶方程（Bianchi方程）的Riemann-Hadamard函数的定义。基于明确表示某些函数的三阶Bianchi方程的Riemann函数的可能性（相对于函数而言），我们为Bianchi方程的系数建立了充分的条件，这些条件提供了Riemann-Hadamard函数的构造就超几何函数而言。