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Problem with Series

  • To: mathgroup at smc.vnet.net
  • Subject: [mg113891] Problem with Series
  • From: Themis Matsoukas <tmatsoukas at me.com>
  • Date: Wed, 17 Nov 2010 05:29:35 -0500 (EST)

I was using Series to linearize a function at x=0 but I run into a problem with the specific function below:

f = Log[Coth[1/2 ArcCosh[Sqrt[1 + x^2]/x]]];
fLinearized = Simplify[Normal[Series[f, {x, 0, 1}]]]
Plot[{f, fLinearized, x}, {x, -10, 10}]

Mathematica produces output without complaining but the result does not contain an explicit linear term. Specifically, fLinearized is not a linear function of x, though it does seem to have the same derivative at x=0 as the original function f. The correct answer should be f=x +O[x^2].

Themis


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