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Re: Problem with Series

• To: mathgroup at smc.vnet.net
• Subject: [mg113955] Re: Problem with Series
• From: Themis Matsoukas <tmatsoukas at me.com>
• Date: Fri, 19 Nov 2010 05:09:18 -0500 (EST)

That's interesting but it creates more questions than it answers:

1. If I include the second term of the expansion, this method does not work any more:

f = Log[Coth[1/2 ArcCosh[Sqrt[1 + x^2]/x]]];
Series[f, {x, 0, 2}]
fLinearized = FullSimplify[Normal[%]]
fLinearizedLinearized = Normal[Series[fLinearized, {x, 0, 2}]]

Series produces what looks like a power series, but Normal returns a single non linear function, not a polynomial in x. 

2. If I replace FullSimplify with Simplify in your original solution, the second series does not work.

Incidentally, I was able to obtain the full power series by expressing the original function in different form. My question here is really about how Mathematica does things.  

Themis

Themis