Abstract
The exp-log functions of variables, x, y l,. .., y n are those given by expressions with signature K, x, y 1,..., yn, +, −, ×, ÷, exp, log. Given n such functions, F 1,..., F n , the implicit function theorem guarantees the existence of roots y 1 = y 1(x),..., y n = y n (x) of the equations F 1 = 0,..., F n = 0 in a neighbourhood of any solution point where the rank of the Jacobian matrix is maximal. The root functions y 1 = y 1 (x),..., y n = y n (x) are called implicit functions. We wish to be able to calculate the asymptotics of implicit functions in neighbourhoods of +∞, that is to say on intervals of the form (a, ∞).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Shackell, J.R. (2004). Implicit Functions. In: Symbolic Asymptotics. Algorithms and Computation in Mathematics, vol 12. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-10176-6_8
Download citation
DOI: https://doi.org/10.1007/978-3-662-10176-6_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05925-4
Online ISBN: 978-3-662-10176-6
eBook Packages: Springer Book Archive