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>