# Why was Indicial equations named so?

In ODE, in Frobenius method, there's an equation called "Indicial Equation." Is there any particular contextual/historical reason that it is named so?

"Indicial" is derived from "indices", in this case indices of the coefficients. The Latin word indicium originally meant a sign, indicator. "Indicial equation" is most often used in the context of solving equations of the form $$a_nx^n\frac{d^n}{dx^n}+\dots+a_1x\frac{dy}{dx}+a_0y=0$$. A substitution, known already to Euler, reduces it to a linear equation with constant coefficients, and the characteristic equation of the latter is called the "indicial equation" of the original.
Euler, who gave a general method for solving these types of equations, used neither the term nor the notation. Most notably, his coefficients did not have the subscripts, like $$a_n$$, making the arguments somewhat cumbersome. In modern notation, the indicial equation is formed directly from the indexed coefficients. In What′s in a Name: Why Cauchy and Euler Share the Cauchy–Euler Equation Parker quotes Sandifer's view of the significance of that (from his Some Facets of Euler’s work on Series, in the volume Leonhard Euler: Life, Work and Legacy volume):