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