Cauchy–Euler operator

{{one source |date=April 2024}}

In mathematics a Cauchy–Euler operator is a differential operator of the form $p(x)\backslash cdot\{d\; \backslash over\; dx\}${{cite book|last=Ross|first=Clay C|title=Differential Equations: An Introduction with Mathematica|year=2004|publisher=Springer|isbn=9781441919410}} 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.