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

Out=
2
(x + I y)
SeriesData[u, 0, {1, 0, ----------}, 0, 3, 1]
2

In:= ComplexExpand[Re[Normal@s]]

Out=
2  2    2  2
u  x    u  y
1 + ----- - -----
2       2

In:= ComplexExpand[Im[Normal@s]]

Out=
2
u  x y

--
Jean-Marc

```

• Prev by Date: Re: Simplifying the exponents
• Next by Date: Re: Simplifying the exponents
• Previous by thread: Re: How to get the real and imaginary parts of a power series?
• Next by thread: Re: How to get the real and imaginary parts of a power series?