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
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