On the Multiplicative Property of Indicial Polynomials

The roots of the indicial polynomial constructed for a given linear ordinary differential operator provide information on the singularities of the solutions of the corresponding homogeneous differential equation. Operators and equations whose coefficients are formal Laurent series are discussed. Solutions of the same type are also considered. Under these assumptions, the structure of the indicial polynomial of the product of differential operators is described. This structural (multiplicative) property is preserved in the case of convergent series.