Cauchy-Euler equation

There is a difference equation analogue to the Cauchy-Euler equation.

In mathematics, a Cauchy-Euler equation (also known as the Euler-Cauchy equation, or simply Euler's equation) is a linear homogeneous ordinary differential equation with variable coefficients.

The most common Cauchy-Euler equation is the second-order equation, appearing in a number of physics and engineering applications, such as when solving Laplace's equation in polar coordinates.