# A nonlinear differential operator series that commutes with any function

@inproceedings{Olver1992AND, title={A nonlinear differential operator series that commutes with any function}, author={Peter J. Olver}, year={1992} }

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… CONTINUE READING

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## Canonical Forms for Bihamiltonian Systems

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