# 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}
}
• Peter J. Olver
• Published 1992
• Mathematics
• 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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## Sur Deux Formules De Frobenius et Stickelberger et Inversion De Lagrange

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• 2013

## SPECTRAL RESIDUES OF SECOND-ORDER DIFFERENTIAL EQUATIONS: A NEW METHODOLOGY FOR SUMMATION IDENTITIES AND INVERSION FORMULAS.

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CITES METHODS

## Canonical Forms for Bihamiltonian Systems

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## Now, to complete the proof of Theorem 4, it suffices to notice that '(u), as defined by (A1), being a particular case of (A2), satisfies the three conditions of Lemma A3

• But then the series @('(u)) also satisfies them since, for example, r((u)) '((u))y((u)) o

## Then , are uniquely determined by the function Vo(Uo)= @(Uo)

• Then , are uniquely determined by the function Vo(Uo)= @(Uo)