# A nonlinear differential operator series that commutes with any function

@article{Olver1992AND,
title={A nonlinear differential operator series that commutes with any function},
author={P. Olver},
journal={Siam Journal on Mathematical Analysis},
year={1992},
volume={23},
pages={209-221}
}
• P. Olver
• Published 1992
• Mathematics
• Siam Journal on Mathematical Analysis
A natural differential operator series is one that commutes with every function. The only linear examples are the formal series operators $e^{\alpha zD}$ representing translations. This paper discusses a surprising natural nonlinear “normally ordered” differential operator series, arising from the Lagrange inversion formula. The operator provides a wide range of new higher-order derivative identities and identities among Bell polynomials. These identities specialize to a large variety of… Expand
11 Citations

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