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Re: RE: Trigonometric simplification - newbe question

• To: mathgroup at smc.vnet.net
• Subject: [mg49082] Re: [mg49031] RE: [mg49004] Trigonometric simplification - newbe question
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Wed, 30 Jun 2004 05:34:28 -0400 (EDT)
• Reply-to: hanlonr at cox.net
• Sender: owner-wri-mathgroup at wolfram.com

expr=(4*(2*a*Sin[(n*Pi)/2]-a*Sin[n*Pi]))/(n^2*Pi^2);

Simplify[expr, Element[n, Integers]]

(8*a*Sin[(n*Pi)/2])/(n^2*Pi^2)

If n is even

FullSimplify[% /. n->2m, Element[m, Integers]]

0

If n is odd

FullSimplify[%% /. n->2m+1, Element[m, Integers]]

(8*(-1)^m*a)/(2*Pi*m + Pi)^2


Bob Hanlon

> 
> From: "David Park" <djmp at earthlink.net>
To: mathgroup at smc.vnet.net
> Date: 2004/06/29 Tue AM 04:50:08 EDT
> To: mathgroup at smc.vnet.net
> Subject: [mg49082] [mg49031] RE: [mg49004] Trigonometric simplification - newbe 
question
> 
> Walter,
> 
> Add an assumption to Simplify (In Version 5, at least).
> 
> expr = (4*(2*a*Sin[(n*Pi)/2] - a*Sin[n*Pi]))/(n^2*Pi^2);
> 
> Simplify[expr, n \[Element] Integers]
> (8*a*Sin[(n*Pi)/2])/(n^2*Pi^2)
> 
> But I don't know how one would specify in the assumptions that n was an 
even
> integer greater than zero, say.
> 
> David Park
> djmp at earthlink.net
> http://home.earthlink.net/~djmp/
> 
> 
> 
> From: Christensen [mailto:fedderwi at uni-bremen.de]
To: mathgroup at smc.vnet.net
> To: mathgroup at smc.vnet.net
> 
> Hi,
> 
> this is a Mathematica newbe question for sure:
> 
> Mathematica comes up with the following result:
> 
>        (4*(2*a*Sin[(n*Pi)/2] - a*Sin[n*Pi]))/(n^2*Pi^2)
> 
> Now I have the additional assumption that n is element of
> {1,2,3, ...) (and a is real)
> 
> How do I tell Mathematica to take this into consideration and
> remove the Sin[n*Pi] term?
> 
> Thanks,
> Walter
> 
> Trigonometric simplification - newbe question
> 
> 
> 
>