Re: How to get the real and imaginary parts of a power series?
- To: mathgroup at smc.vnet.net
- Subject: [mg80007] Re: How to get the real and imaginary parts of a power series?
- From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
- Date: Fri, 10 Aug 2007 06:37:53 -0400 (EDT)
- Organization: The Open University, Milton Keynes, UK
- References: <f9gvbc$b90$1@smc.vnet.net>
Gordon Smith wrote:
> 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!)
You are almost there: apply *Normal* to your series (a series data
object, indeed) and then Re or Im followed by ComplexExpand.
In[1]:= s = Series[Cosh[(x + I y) u], {u, 0, 2}]
Out[1]=
2
(x + I y)
SeriesData[u, 0, {1, 0, ----------}, 0, 3, 1]
2
In[2]:= ComplexExpand[Re[Normal@s]]
Out[2]=
2 2 2 2
u x u y
1 + ----- - -----
2 2
In[3]:= ComplexExpand[Im[Normal@s]]
Out[3]=
2
u x y
--
Jean-Marc