English

Deriving Fa\`a di Bruno's formula for the derivative of a composite function via compositions of integers

Combinatorics 2014-03-04 v1

Abstract

We give yet another proof for Fa\`{a} di Bruno's formula for higher derivatives of composite functions. Our proof technique relies on reinterpreting the composition of two power series as the generating function for weighted integer compositions, for which a Fa\`{a} di Bruno-like formula is quite naturally established.

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@article{arxiv.1403.0519,
  title  = {Deriving Fa\`a di Bruno's formula for the derivative of a composite function via compositions of integers},
  author = {Steffen Eger},
  journal= {arXiv preprint arXiv:1403.0519},
  year   = {2014}
}

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