A note on the roots of the indicial equation

الملخص EN

When a second or higher order linear homogeneous differential equation is solved by the Frobenius’ method near a regular singular point, the sum of the roots of the indicial equation determine the behaviour of the Wronskian at that point.

If « is either an ordinary or a regular singular point and all singular points are regular then the global restrictions on the Wronskian force some conditions on the sum of the roots of the indicial equations at different points.

In this note this condition is found and proven.