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

• To: mathgroup at smc.vnet.net
• Subject: [mg80010] RE: [mg79998] How to get the real and imaginary parts of a power series?
• From: "Jaccard Florian" <Florian.Jaccard at he-arc.ch>
• Date: Fri, 10 Aug 2007 06:39:26 -0400 (EDT)
• References: <200708100552.BAA10970@smc.vnet.net>

Hello Gordon,

I think the problem is because of O(u^3) which makes it difficult to do 
further job with s.

This works fine, but there is no O(u^3) anymore written :

Clear[s]
s = Normal[Series[Cosh[(x + I*y)*u], {u, 0, 2}]]

ComplexExpand[s]


Regards

Florian Jaccard

-----Message d'origine-----
De=A0: Gordon Smith [mailto:gsmithsf at hotmail.com]
Envoy=E9=A0: vendredi, 10. ao=FBt 2007 07:53
=C0=A0: mathgroup at smc.vnet.net
Objet=A0: [mg79998] How to get the real and imaginary parts of a power series?

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!)

• References:
  • How to get the real and imaginary parts of a power series?
    • From: Gordon Smith <gsmithsf@hotmail.com>