1819/12/31 by W.G. Horner, William George Horner · 4 citations
Engineering · Mathematics · #Differential Equations and Boundary Problems #History and Theory of Mathematics #Material Science and Thermodynamics
paper · doi:10.1098/rstl.1819.0023
crossref issued 1819/12/31 · crossref published 1819/12/31 · crossref published-print 1819/12/31 · openalex publication_date 1819/12/31 · crossref created 2006/12/18 · openalex created_date 2020/10/15 · crossref deposited 2026/02/27 · openalex updated_date 2026/07/31 · crossref indexed 2026/08/05
Abstract 1. The process which it is the object of this Essay to establish, being nothing else than the leading theorem in the Calculus of Derivations, presented under a new aspect, may be regarded as a universal instrument of calculation, extending to the composition as well as analysis of functions of every kind. But it comes into most useful application in the numerical solution of equations. 2. Arbogast’s developement of ϕ ( α + βx + γx2 + δx3 + ∈x4 + .... ) (See Calc, des Der. § 33 ) supposes all the coefficients within the parenthesis to be known previously to the operation of ϕ. To the important cases in which the discovery of γ, δ, &c. depends on the previous developement of the partial functions ϕ ( α + βx ), ϕ ( α + βx + γx2), &c.