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Re: Sums and Products: Compact Notation and Differentiation
*To*: mathgroup at smc.vnet.net
*Subject*: [mg23941] Re: Sums and Products: Compact Notation and Differentiation
*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
*Date*: Fri, 16 Jun 2000 00:57:27 -0400 (EDT)
*Organization*: Universitaet Leipzig
*References*: <8i9qoc$2oh@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
Hi,
it is possible but you have to do it by your self because
simply
Clear[sum]
sum /: D[sum[a_, range_], x_] /; FreeQ[range, x] := sum[D[a, x], {i, n}]
will do it but
a) what is with the index shifts ? the {i,n} iterator mean {i,1,n} and
this works only for the first derivative of the sum, with a sum
over {i,0,n} your equations is not true and for a power series
one have
D[sum[a_*x^i_,{i_,n1_,n2_}],x] /; FreeQ[{i,n1,n2},x]:=
sum[D[a*x^i],x],{i,n1+1,n2}]
because the i=0 term depends not on x
b) how to "normalize" expressions like
sums of sum[] ? collect them ? shift the index in the terms
until one can make a sum[a,i]+sum[b,i] :> sum[a+b,i]
Regards
Jens
Justus Piater wrote:
>
> Hi,
>
> I am relatively new to Mathematica (Version 3.0), and have been able
> to get sensible results using expressions involving Sum and Product
> symbols only if the summation/multiplication ranges are given by
> constants. I have the following specific problems:
>
> 1. When I have Mathematica operate on a formula involving Sum and
> Product symbols with constant ranges, it always displays the result
> in expanded form, without these symbols, even though it often seems
> easily possible and much more compact to use Sums and Products. Is
> is possible to have Mathematica retain the convenient notation, and
> prevent it from expanding the terms?
>
> 2. I can't get Mathematica to give me simple derivatives of
> expressions involving Sums and Products, unless the ranges are
> known to Mathematica so it can expand them. For example, I would
> like to type:
>
> D[Sum[Subscript[a,i]x^i,{i,n}],x]
>
> and get as output some rendering of:
>
> Sum[i Subscript[a,i]x^(i-1),{i,n}]
>
> Is this really not possible?
>
> Thanks,
> Justus
>
> --
> Justus Piater Laboratory for Perceptual Robotics U of Mass
> www.cs.umass.edu/~piater Computer Vision Laboratory Amherst
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