RE: sum problem with infinity

• To: mathgroup at smc.vnet.net
• Subject: [mg33019] RE: [mg33002] sum problem with infinity
• From: "David Park" <djmp at earthlink.net>
• Date: Tue, 26 Feb 2002 04:35:02 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Doron,

You must do the differentiation first and then substitute. Also Sum has the
Attribute HoldAll so to get the derivative evaluated in the sum you must
take some measures. In the rule it is necessary to put the left hand side in
a HoldPattern, otherwise Mathematica tries to evaluate the pattern. This
gets you part way to your goal:

D[\[Psi][x, y], y]
% /. HoldPattern[Sum[a_, b_]] :> Sum[Evaluate[a], b]
% /. y -> 0.9 /. x -> 0.8

David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/

> -----Original Message-----
> From: Doron [mailto:klepachd at yahoo.com]
To: mathgroup at smc.vnet.net
> Sent: Monday, February 25, 2002 1:31 AM
> To: mathgroup at smc.vnet.net
> Subject: [mg33019] [mg33002] sum problem with infinity
>
>
> hello,
> I am a problem :
> I defined ->
> \!\(\[Psi][x_, y_] := \(1\/4\) a\^2 -
>       x\^2 - \(\(8
>                a\^2\)\/\[Pi]\^3\) \(\[Sum]\+\(n = \
> 0\)\%\[Infinity]\(\((\(-1\))\)\^n\/\((2  n + 1)\)\^3\) \(Cosh[k[n]*y]\ \
> Cos[k[n]*x]\)\/Cosh[\(1\/2\) k[n]\ b]\)\)
> and tried to compute ->
> D[\[Psi][x, y], y] /. y -> 0.9 /. x -> 0.8
> the answer I got was ->
> General::"ivar": "\!\(0.9`\) is not a valid variable."
>
> General::"stop": "Further output of \!\(General :: \"ivar\"\) will be \
> suppressed during this calculation."
>
> \!\(\(-\(\(32\ \(\[Sum]\+\(n = \
> 0\)\%\[Infinity]\[PartialD]\_0.9`\(\(\((\(-1\))\)\^n\ \((Cosh[
>                           k[n]\ 0.9`]\ Cos[
>                           k[n]\ 0.8`])\)\)\/\(\((2\ n + 1)\)\^3\ Cosh[
>                       1\/2\ k[n]\ b]\)\)\)\)\/\[Pi]\^3\)\)\)
> But when I replaced the sums limit from infinity to 99
> there was no problem and I got a numerical answer.
> Any ideas why ?
> Thank you , Doron .
>

```

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