On the Construction of a Solution of a Horn‐Type System in the Form of Polynomials of Two Variables

ABSTRACT This paper considers a generalized system of second‐order partial differential equations of hypergeometric type that encompasses all 34 Horn series in two variables. Using the modified FrobeniusLatysheva method, we analyze the behavior of solutions near singular points and curves. Conditions for the existence and structure of solutions in the form of generalized power series are obtained, along with recurrence relations for the coefficients. Examples of hypergeometric functions of types , and are provided to validate the proposed approach. The results are of interest for studies in mathematical physics and the theory of special functions.