Taylor expansion for inverse of a defined function
Subject: Taylor expansion for inverse of a defined function
From: K. B. Erickson
Date: Sun, 5 Aug 2012 12:37:36 -0700
In wxMaxima, I have defined a function f(x): = 'expression'. This function
is analytic and odd so it has an analytic inverse defined in a ngbd. of the
origin. Call the inverse g(x). So: f(g(x)=x, g(f(x)=x. I want to compute
some of the Taylor coefficients for g(x) . I can do this by hand at least
for a small number of terms, but there ought to be a way to automate this
using wxMaxima. Keep in mind I only have a "nice" expression for f(x) and
only know g(x) via the defining relations: f(g(x))=x, g(f(x))= x.
kbe