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How to simplify an expression in version 5

• To: mathgroup at smc.vnet.net
• Subject: [mg59022] How to simplify an expression in version 5
• From: "passwd9" <david at carter-hitchin.clara.co.uk>
• Date: Wed, 27 Jul 2005 01:24:43 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Hi,

I'm trying to simplify the expression that comes out of the
FourierTrigSeries function, and I've tried 'Simplify', 'Collect' and
'Factor' but no luck.  My input is as follows:

<< Calculus`FourierTransform`
FourierTrigSeries[Cos[t], t, 5, FourierParameters -> {0, 1/Pi}]

And the output is:

\!\(\(2\/\@\[Pi] + \(4\ Cos[2\ t]\)\/\(3\ \@\[Pi]\) - \(4\ Cos[4\
t]\)\/\(15\ \
\@\[Pi]\) + \(4\ Cos[6\ t]\)\/\(35\ \@\[Pi]\) - \(4\ Cos[8\ t]\)\/\(63\
\@\
\[Pi]\) + \(4\ Cos[10\ t]\)\/\(99\ \@\[Pi]\)\)\/\@\[Pi]\)

That's rather horrid looking in ascii, so I'll try to make something
more readable:

(2/Sqrt(Pi) + 4Cos(2t)/3Sqrt(Pi) - 4Cos(4t)/15Sqrt(Pi) + ... )
---------------------------------------------------------------
                            Sqrt(Pi)


Now the Sqrt(Pi) in the denominator could be 'brought up' into the
terms in the numerator to give:


(2/Pi + 4Cos(2t)/3Pi - 4Cos(4t)/15Pi + ... )

Much more elegant!  Anyone know if MM can do this?

Thanks.

• Follow-Ups:
  • Re: How to simplify an expression in version 5
    • From: yehuda ben-shimol <bsyehuda@gmail.com>