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Localizability of differential operators a la Grothendieck

Hello, Maybe this question is trivial, so sorry Let $A$ be a (comm. with 1) $k$-algebra, where $k$ is a ring (comm. with 1). Then we can define the module of differential operators $D^{\leq n} ...
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Some help with differential operators

Hello I am trying to follow the derivation of the Generalized Cornish Fisher Expansion from this paper. I dont see how the author goes from equation (21) to (22). For one to be able to do this ...