Cauchy–Euler operator

In mathematics a Cauchy–Euler operator is a differential operator of the form $$p(x)\cdot{d \over dx}$$ for a polynomial p. It is named after Augustin-Louis Cauchy and Leonhard Euler. The simplest example is that in which p(x) = x, which has eigenvalues n = 0, 1, 2, 3, ... and corresponding eigenfunctions xn.