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MathGroup Archive 2005

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Re: evaluate assuming odd integers?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg58986] Re: evaluate assuming odd integers?
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Tue, 26 Jul 2005 04:01:51 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, England
  • References: <dc1t2f$4v8$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

ab at sd.com wrote:
> Is there a way in Mathematica to evaluate an expression assuming some 
> varialbe is Odd integer, for example in below integral how can i tell it 
> that n is odd integer in the Assumptions section of FullSimplify command or 
> the integral itself??:
> In[35]:=
> Integrate[Sin[n*Pi*(z/L)], {z, 0, L}]
> FullSimplify[%, n \[Element] Integers && n >= 0 &&
> L \[Element] Reals && L > 0 && z \[Element] Reals]
> 

Replace n by 2*k+1, k being any non-negative integer:

In[1]:=
Integrate[Sin[(2*k + 1)*Pi*(z/L)], {z, 0, L}, Assumptions -> {k â?? 
Integers && k >= 0 && L > 0 && z â?? Reals}]

Out[1]=
(2*L)/(Pi + 2*k*Pi)

Regards,
/J.M.


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