The Curious History of Faà di Bruno's Formula

By Warren P. Johnson. The American mathematical monthly, 2002

656 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Theoretical Computer Science

View Paper: https://www.semanticscholar.org/paper/00f6bd8e77f7c51e7626dd56dc4d93e258da7f70

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Citations in the corpus

The coalescent structure of continuous-time Galton–Watson trees (2017, methodology): “14), by making reference to Faà Di Bruno’s formula [23].”
Higher order averaging theory for finding periodic solutions via Brouwer degree (2014, methodology): “In the proof of Lemma 1 we use the Faá di Bruno’s Formula (see [14]), about the l derivative of a composite function.”
Solution of Delay Differential Equation by Means of Homotopy Analysis Method (2009, neutral): “, jm−k = k and j1 + 2j2 + · · · + (m− k)jm−1 [27, 28].”
Chain rules for higher derivatives (2006, background): “FaA di Bruno's formula, and others given in [8], have a substantial combinatorial aspect; a less combinatorial and general ly more transparent treatment is that of Spindler [11].”
Advanced Determinant Calculus: A Complement (2005, background): “nding results. Further reduction formulae and determinant evaluations from [33] address determinants of matrices formed out of coeﬃcients of iterated compositions of formal power 21As one can read in [92], “Faa` di Bruno was neither the ﬁrst to state the formula that bears his name nor the ﬁrst to p”
Stochastic and geometric analysis of two infinite-dimensional groups (2010, neutral): “9 (Faà di Bruno’s formula [17]).”
A PROPERTY OF LOGARITHMICALLY ABSOLUTELY MONOTONIC FUNCTIONS AND THE LOGARITHMICALLY COMPLETE MONOTONICITY OF A POWER-EXPONENTIAL FUNCTION (2009, neutral): “(1) For α 0, Fα,β(x) ∈ CL[(−α,∞)] if and only if β ≤ α and 1 Fα,β(x) ∈ CL[(−α,∞)] if and only if 2β ≥ α. (2) For α > 0, Fα,β(x) ∈ CL[(0,∞)] if and only if 2β ≥ α and 1Fα,β(x) ∈ CL[(0,∞)] if and only if β ≤ 0.”
The Lah Numbers and the nth Derivative of e1/x (2013, background): “However, neither contains a proof of the formula (merely its statement), and Faà di Bruno was not actually the first to state the formula or to prove it! Readers interested in learning more should consult Warren Johnson’s paper “The curious history of Faà di Bruno’s formula” [6].”
Arithmetic Operations on Independent Random Variables: A Numerical Approach (2012, methodology): “The proof (except for the last part) will use Faà di Bruno’s formula [15] for the nth derivative of the composition of two functions”