ON THE MULTIPLICATIVE PROPERTY OF DEFINING POLYNOMIALS

The roots of the indicial polynomial constructed for a given linear ordinary differential operator provide information about the features of solutions of the corresponding homogeneous differential equation. Operators and equations whose coefficients are formal Laurent series are discussed. Solutions of the same kind are considered. These assumptions describe the structure of the indicial polynomial of the product of differential operators. This structural (multiplicative) property is preserved in the case of converging series.

linear ordinary homogeneous differential equations, defining polynomial, formal Laurent series, induced recurrent operators