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In mathematics a Cauchy–Euler operator is a differential operator of the form $p(x)\cdot \frac{d}{dx}$ 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.

See also

• Cauchy–Euler equation
• Sturm–Liouville theory

References

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