BibTeX
@ARTICLE{
Neidinger2013Err,
title = "Efficient recurrence relations for univariate and multivariate Taylor series
coefficients",
author = "Richard D. Neidinger",
publisher = "AIMS",
year = "2013",
journal = "Dynamical Systems and Differential Equations",
volume = "Special, Proceedings of the 9th AIMS International Conference (Orlando, USA)",
pages = "587596",
abstract = "The efficient use of Taylor series depends, not on symbolic differentiation, but on
a standard set of recurrence formulas for each of the elementary functions and operations. These
relationships are often rediscovered and restated, usually in a piecemeal fashion. We seek to
provide a fairly thorough and unified exposition of efficient recurrence relations in both
univariate and multivariate settings. Explicit formulas all stem from the fact that multiplication
of functions corresponds to a Cauchy product of series coefficients, which is more efficient than
the Leibniz rule for nthorder derivatives. This principle is applied to function relationships of
the form h'=v*u', where the prime indicates a derivative or partial derivative. Each
standard (calculator button) function corresponds to an equation, or pair of equations, of this
form. A geometric description of the multivariate operation helps clarify and streamline the
computation for each desired multiindexed coefficient. Several research communities use such
recurrences including the Differential Transform Method to solve differential equations with initial
conditions.",
url = "http://aimsciences.org/journals/displayPaperPro.jsp?paperID=9241",
ad_theotech = "General, Taylor Arithmetic"
}
