Abstract
Concepts of higher-order differentiation of functions and jet fields, of vector fields, and of covecter fields are introduced. These concepts, which generalize those of successive differentiation (ordinary or covariant), are shown to correspond to certain important types of derivative strings.
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Barndorff-Nielsen, O.E., Blæsild, P. & Mora, M. Generalized higher-order differentiation. Acta Appl Math 16, 243–259 (1989). https://doi.org/10.1007/BF00052519
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DOI: https://doi.org/10.1007/BF00052519