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Re: If and Piecewise don't quite do what I need

  • To: mathgroup at smc.vnet.net
  • Subject: [mg113432] Re: If and Piecewise don't quite do what I need
  • From: Bill Rowe <readnews at sbcglobal.net>
  • Date: Thu, 28 Oct 2010 04:27:56 -0400 (EDT)

On 10/27/10 at 5:15 AM, sam.takoy at yahoo.com (Sam Takoy) wrote:

>I have found that If doesn't do winside it like I would want it to
>do. Piecewise does do it, but then it doesn't work the way I would
>want it. Is there a solution that does both?

>Example:

>c[n_] := Piecewise[{{1, {n, 0}}},
>Integrate[a^2 Cos[n a], {a, -Pi, Pi}]]
>c[n] (* Calculates the Integral *)
>Sum[c[n], {n, 0, Infinity}] (* But fails to Sum *)
>d[n_] := If[n == 0, 1, Integrate[a^2 Cos[n a], {a, -Pi, Pi}]]
>(* Fails to calculate the integral *)
>d[n] (* But does sum OK *)
>Sum[d[n], {n, 0, Infinity}]

>I want it to evaluate the integral and to sum properly.

Instead of using either Piecewise or If why not do:

In[5]:= d[0] = 1;
d[n_] = Integrate[a^2 Cos[n a], {a, -Pi, Pi}];

In[7]:= Sum[d[n], {n, 0, \[Infinity]}]

Out[7]= Pi^3/3

Note, I use Set (=) not SetDelayed (:=) when defining d. This
avoids any need to re-compute the integral when doing the summation.



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