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Re: simplification rule for infinite sum

  • To: mathgroup at smc.vnet.net
  • Subject: [mg105813] Re: [mg105799] simplification rule for infinite sum
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Sun, 20 Dec 2009 06:53:58 -0500 (EST)
  • Reply-to: hanlonr at cox.net

expr = a Sum[(n + 2) c[n] x^n, {n, 5, Infinity}] +
   b Sum[(n + 2) (n + 1) c[n] x^n, {n, 5, Infinity}];

expr /. c1_*Sum[expr1_, iter_List] +
   c2_*Sum[expr2_, iter_List] :>
 
  Sum[Simplify[c1*expr1 + c2*expr2], iter]

Sum[(n + 2)*c[n]*x^n*(a + b*n + b), {n, 5, Infinity}]


Bob Hanlon

---- "Ruth Lazkoz S=C3=A1ez" <ruth.lazkoz at ehu.es> wrote:

=============
Hi,

I have managed to define rules with patterns to shift indexes on the
coefficients of infinite sums, but I have failed to
do something so apparently simple as making Mathematica understand that this


a Sum[(n + 2) c[n] x^n, {n, 5, Infinity}] +
 b Sum[(n + 2) (n + 1) c[n] x^n, {n, 5, Infinity}]

should be simplified to this

Sum[(n + 2) (a + b (n + 1)) c[n] x^n, {n, 5, Infinity}]

Can someone help me?  Thanks a lot,

Ruth Lazkoz



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