Re: Converting the integral of a sum into a sum of integrals

*To*: mathgroup at smc.vnet.net*Subject*: [mg109090] Re: Converting the integral of a sum into a sum of integrals*From*: "David Park" <djmpark at comcast.net>*Date*: Mon, 12 Apr 2010 23:00:04 -0400 (EDT)

I don't know why you have patterns in the rhs of the rule. In any case, the following works. I set the a_i coefficients to 1 in the last step to obtain a complete evaluation. HoldForm@Integrate[ Sum[Times[Power[x, i], Subscript[a, i]], {i, 0, k}], x] % /. Integrate[Sum[term_, range_], variable_] :> Sum[Integrate[term, variable], range] % // ReleaseHold % /. Subscript[a, i] -> 1 David Park djmpark at comcast.net http://home.comcast.net/~djmpark/ From: Kurt TeKolste [mailto:tekolste at fastmail.net] If I ask Mathematica to perform an indefinite integrate on a symbolic summation (with terms of the form a_i x^i), Integrate[Sum[Times[Power[x,i],Subscript[a,i]],{i,0,k}], it does nothing. If I try to tell it that summation and integration commute by applying the rule: Integrate[Sum[term_,range_],variable_]-> Sum[Integrate[term_,variable_],range_] I get a strange result equivalent to term * range or, in this case, Times[Power[x,i],Subscript[a,i]] * {i,0,k} or {i a_i x^i, 0, k a_i x^i} Any ideas as to what's going on? (BTW: 1) If you use rules to extract each of term, range, and variable and then take Sum[Integral[...],...] the correct answer is returned. 2) if you use a rule that changes Sum to Power, i.e. Integrate[Sum[term_,range_],variable_] -> Product[Integrate[term_,variable_],range_] you get exponents term^(range - 1) Odd... ) ekt