Re: D under Sum

*To*: mathgroup at smc.vnet.net*Subject*: [mg128431] Re: D under Sum*From*: Daniel <dosadchy at its.jnj.com>*Date*: Fri, 19 Oct 2012 02:41:23 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net

> Hello > > I want the derivation D to be applied under the Sum > sign, > I have a function HoldSum that do not evaluate but is > similar to Sum in form > > In[3]:= D[HoldSum[p*i, {i, 1, n}], p] > > I get the output : > > Out[3]=i*HoldSum^(1, {0, 0, 0})[i p, {i, 1, n}] > > but I would want that D be applied under the Sum sign > like done by hand here : > > In[5]:= HoldSum[D[p i, i], {i, 1, n}] > > Out[5]= HoldSum[p, {i, 1, n}] > > Obviously I want D to work for any expression > containing HoldSum (even on nested HoldSum > expression) > > Does anybody knows how to do that ? > > Best regards > > Nicolas > I don't understand why you want derivative with respect to 'p' (D[HoldSum[p*i, {i, 1, n}], p]) to be replaced by derivative with respect to 'i' (HoldSum[D[p i, i], {i, 1, n}]) Assuming you meant HoldSum[D[p i, p], {i, 1, n}], you should define a delayed upvalue: In[1]:= D[HoldSum[s_,i_],v_] ^:= HoldSum[D[s,v],i] In[2]:= D[HoldSum[p*i,{i,1,n}],p] Out[2]= HoldSum[i,{i,1,n}] In[4]:= D[HoldSum[p^i,{i,1,n}],p] Out[4]= HoldSum[i p^(-1+i),{i,1,n}]