Re: Problem with sums differentiation

• To: mathgroup at smc.vnet.net
• Subject: [mg13277] Re: [mg13143] Problem with sums differentiation
• From: "Jens-Peer Kuska" <kuska at linmpi.mpg.de>
• Date: Fri, 17 Jul 1998 03:18:21 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```Hi Dimitri,

The rule that gives the desired result is

D[a[x,t],x] /. HoldPattern[Sum[D[a_,x_],iter_]]
:>Sum[Evaluate[D[a,x]],iter]

the total derivative Dt[] is not needed here. Sum has the attribute
HoldAll and will
by default not evaluate its arguments.

Hope that helps
Jens

-----Original Message-----
From: Dmitri Tcherniak <famdt at pop.dtu.dk> To: mathgroup at smc.vnet.net
Subject: [mg13277] [mg13143] Problem with sums differentiation

>
>I have problems with infinite sums integration, differentiations,
>multiplications when the imax is infinity or a symbol. For example
>
>In:
>a[x_,t_]=Sum[uj[t]*Cos[j Pi x],{j,1,Infinity}]; Dt[a[x,t],x]
>
>gives me
>Out: Dt[Sum[uj[t] Cos[j Pi x], {j, 1, Infinity}], x]
>
>but not something like Sum[-uj[t]*j*Pi*Sin[j Pi x],{j,1,Infinity}]
>
>Is there a way to move the integration (differentiation) sigh under the
>sum sigh and force Mathematica to evaluate the terms?
>
>Thank you
>Dmitri Tcherniak
>
>
>

```

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