Re: Problem with sums differentiation

• To: mathgroup at smc.vnet.net
• Subject: [mg13269] Re: Problem with sums differentiation
• From: "Allan Hayes" <hay at haystack.demon.cc.uk>
• Date: Fri, 17 Jul 1998 03:18:02 -0400
• References: <6ocqtm\$gps@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Dmitri Tcherniak wrote in message <6ocqtm\$gps at smc.vnet.net>...
>
>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
>
>

Dmitri,

Here are three ways

a[x_,t_] =
Sum[uj[t]*Cos[j Pi x],{j,1,Infinity}];

(1)
a[x,t]/.h_[b_,r__]:>h[Evaluate[ Dt[b,x]],r]

Sum[-((j Pi + Pi x Dt[j, x]) Sin[j Pi x] uj[t]) +

Cos[j Pi x] Dt[t, x] uj'[t], {j, 1, Infinity}]

(2)
MapAt[Evaluate,MapAt[Dt[#,x]&, a[x,t], {{1}}],{{1}}]

Sum[-((j Pi + Pi x Dt[j, x]) Sin[j Pi x] uj[t]) +

Cos[j Pi x] Dt[t, x] uj'[t], {j, 1, Infinity}]

(3)
Sum@@List@@MapAt[Dt[#,x]&, a[x,t], {{1}}]

Sum[-((j Pi + Pi x Dt[j, x]) Sin[j Pi x] uj[t]) +

Cos[j Pi x] Dt[t, x] uj'[t], {j, 1, \[Infinity]}]

------------------------------------------------------------- Allan
Hayes
Training and Consulting
Leicester UK
http://www.haystack.demon.co.uk
hay at haystack.demon.co.uk
voice: +44 (0)116 271 4198
fax: +44(0)116 271 8642

```

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