Re: Derivative of Sum

*To*: mathgroup at smc.vnet.net*Subject*: [mg48006] Re: Derivative of Sum*From*: "Carl K. Woll" <carlw at u.washington.edu>*Date*: Wed, 5 May 2004 08:11:11 -0400 (EDT)*Organization*: University of Washington*References*: <c6o4gn$cju$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Michal, Here is one possibility: Unprotect[D]; D[Subscript[i_,j_],Subscript[i_,k_],NonConstants->{Subscript}]:= DiscreteDelta[j-k] D[Subscript[i_,j_],Subscript[k_,l_],NonConstants->{Subscript}]:=0 D[HoldPattern[Sum[a_,b_]],c__]:=Sum[D[a,c],b] Protect[D]; Then, we have In[8]:= D[Sum[Subscript[a,k]Subscript[b,k],{k,n}],Subscript[a,i],NonConstants->{Subs cript}] Out[8]= b UnitStep[-1 + i] UnitStep[-i + n] i I used Subscript[a,k] to make things legible in this post, but you could of course use real subscripts and things will work. The only problem is that Mathematica doesn't know that i is between 1 and n, so the UnitSteps pop up. You could put in some assumptions, or you could simply extend the range of the sum, as in In[9]:= D[Sum[Subscript[a,k]Subscript[b,k],{k,-Infinity,Infinity}],Subscript[a,i],No nConstants->{Subscript}] Out[9]= b i to get rid of the UnitSteps. Carl Woll "Michal Kvasnicka" <michal.kvasnicka at _NO_ZpaMM-.quick.cz> wrote in message news:c6o4gn$cju$1 at smc.vnet.net... > Is Mathematica 5 able to compute the folowing problem: > \!\(S = Sum[\(a\_k\) b\_k, {k, 1, n}]\) > > then should be > > \!\(\[PartialD]\_\(a\_i\)\ S = b\_i\) but the Mathematica gives 0. > > Thanks, Michal > >