Re: partial derivative of a sum
- To: mathgroup at smc.vnet.net
- Subject: [mg59814] Re: partial derivative of a sum
- From: "James Gilmore" <james.gilmore at yale.edu>
- Date: Mon, 22 Aug 2005 02:48:45 -0400 (EDT)
- Organization: Yale University
- References: <de9cut$q78$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
When you specify Infinity or N below as the upper bound on the sum, it
remains in unevaluated form. Sum has the attribute HoldAll.
This code will get you the desired result:
SumDerivative[ni_, j_] := If[ni > j, 0, D[Sum[n[i]*l[i], {i, 1, j}], n[ni]]]
SumDerivative[ni_, Infinity] := l[ni]
Note that you need to supply the upper bound of the sum.
--
James Gilmore
Graduate Student
Department of Physics
Yale University
New Haven, CT 06520 USA
"Daniel Roy" <droy at MIT.EDU> wrote in message
news:de9cut$q78$1 at smc.vnet.net...
> I'm wondering if Mathematica can handle expressions such as:
>
> ClearAll[n, l]
> D[Sum[n[i] l[i], {i, 1, Infinity}], n[10]]
>
> The answer should be l[10], but Mathematica returns 0.
>
> ClearAll[n, l]
> D[Sum[n[i]l[i], {i, 1, 100}], n[10]]
>
> return l[10] as expected. More generally,
>
> ClearAll[n, l]
> Assumptions[N \[Element] Integers && N>10,
> D[Sum[n[i] l[i],{i,1,N}], n[10]]
>
> Thanks,
> Dan Roy
>
>
>