Re: How to simplify an expression in version 5

*To*: mathgroup at smc.vnet.net*Subject*: [mg59056] Re: How to simplify an expression in version 5*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Thu, 28 Jul 2005 02:26:01 -0400 (EDT)*Organization*: The Open University, Milton Keynes, U.K.*References*: <dc76b4$jpk$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

passwd9 wrote: > 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. > Hi David, The command *ExpandAll* will do the trick: In[1]:= Needs["Calculus`FourierTransform`"] In[2]:= ExpandAll[FourierTrigSeries[Cos[t], t, 5, FourierParameters -> {0, 1/Pi}]] Out[2]= 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) Regards, /J.M.