The multivariate Faà di Bruno formula and multivariate Taylor expansions with explicit integral remainder term

DOI10.1017/S1446181100003527zbMath1149.46036OpenAlexW2160304172MaRDI QIDQ5437202

R. B. Leipnik, Charles E. M. Pearce

Publication date: 18 January 2008

Published in: The ANZIAM Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s1446181100003527

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Continuity and differentiation questions (26B05) Derivatives of functions in infinite-dimensional spaces (46G05)

Related Items (8)

Spaces of polynomial functions of bounded degrees on an embedded manifold and their duals ⋮ Refined decay estimate and analyticity of solutions to the linear heat equation in homogeneous Besov spaces ⋮ Long time semiclassical Egorov theorem for ℏ-pseudodifferential systems ⋮ Computing the region of convergence for power series in many real variables: A ratio-like test ⋮ Some extensions of Faà di Bruno's formula with divided differences ⋮ A new algorithm for computing the multivariate Faà di Bruno's formula ⋮ The ordinary differential equations and automatic differentiation unified ⋮ On the abs-polynomial expansion of piecewise smooth functions

Cites Work

• Derivatives are essentially integer partitions
• Generalization of the formula of Faa di Bruno for a composite function with a vector argument
• From Ford to Faa
• The Curious History of Faa di Bruno's Formula
• A Multivariate Faa di Bruno Formula with Applications
• The Number of Partitions of a Set
• Applications of Faa Di Bruno's Formula in Mathematical Statistics
• Geometric probability
• Unnamed Item

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