The \(n\)th order implicit differentiation formula for two variables with an application to computing all roots of a transcendental function

DOI10.1007/s11786-012-0110-0zbMath1302.65131OpenAlexW1994874615MaRDI QIDQ1948613

John Michael Nahay

Publication date: 24 April 2013

Published in: Mathematics in Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11786-012-0110-0

zbMATH Keywords

Lagrange inversiontranscendental functionimplicit differentiationcountably infinitely many roots of a pseudopolynomialpower series formula

Mathematics Subject Classification ID

General theory of numerical methods in complex analysis (potential theory, etc.) (65E05) Numerical computation of solutions to single equations (65H05)

Related Items (1)

The combinatorics of higher derivatives of implicit functions

Cites Work

• Unnamed Item
• On the efficient computation of high-order derivatives for implicitly defined functions
• Multidimensional Bell polynomials of higher order
• Application of Faà di Bruno's formula in characterization of inverse relations
• Using forward accumulation for automatic differentiation of implicitly-defined functions
• A multivariate Lagrange inversion formula for asymptotic calculations
• Generalization of the formula of Faa di Bruno for a composite function with a vector argument
• Higher chain formula proved by combinatorics
• Formules exprimant les valeurs des coefficients des séries de puissances inverses
• Reverse aumulation and imploicit functions
• The Curious History of Faa di Bruno's Formula
• A Multivariate Faa di Bruno Formula with Applications
• Prehistory of Faà   di Bruno's Formula

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