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How to get the real and imaginary parts of a power series?

• To: mathgroup at smc.vnet.net
• Subject: [mg79998] How to get the real and imaginary parts of a power series?
• From: Gordon Smith <gsmithsf at hotmail.com>
• Date: Fri, 10 Aug 2007 01:52:48 -0400 (EDT)

Suppose s = Series[Cosh[(x + I y)u, {u,0,2}]. How can I get the real part 1 + 1/2(x^2 - y^2) u^2 + O(u^3) and the imaginary part x y u^2 + O(u^3) ? I thought ComplexExpand[Re[s]] should give me the real part of s, but it just gives me s unchanged. (Mathematica newbie here!)

• Follow-Ups:
  • Re: How to get the real and imaginary parts of a power
    • From: Murray Eisenberg <murray@math.umass.edu>
  • RE: How to get the real and imaginary parts of a power series?
    • From: "Jaccard Florian" <Florian.Jaccard@he-arc.ch>