Some inversion formulas for functions and power series (Q1806073)
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scientific article; zbMATH DE number 1356277
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some inversion formulas for functions and power series |
scientific article; zbMATH DE number 1356277 |
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Some inversion formulas for functions and power series (English)
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28 May 2000
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An explicit formula for the \(n\)-fold derivative \((f^{-1})^{(n)}\) of the inverse function \(f^{-1}\) of a given function \(f\) is presented, which generalizes the Lagrange inversion formula concerning the compositional inverse of a power series. The proof is based on combinatorics and is similar to the proof for the chain rule of analytic functions by D. E. Knuth.
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Lagrange inversion formula
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power series
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formula of Faà di Bruno
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