Cauchy–Euler operator explained

In mathematics a Cauchy–Euler operator is a differential operator of the form

p(x) ⋅ {d \over dx} ^[1] 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.

See also

• Cauchy–Euler equation
• Sturm–Liouville theory

Notes and References

1. Book: Ross, Clay C. Differential Equations: An Introduction with Mathematica. 2004. Springer. 9781441919410.