Converting the integral of a sum into a sum of integrals

*To*: mathgroup at smc.vnet.net*Subject*: [mg109064] Converting the integral of a sum into a sum of integrals*From*: "Kurt TeKolste" <tekolste at fastmail.net>*Date*: Mon, 12 Apr 2010 06:53:48 -0400 (EDT)*References*: <201004110831.EAA06714@smc.vnet.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

**References**:**Re: Symplify Table***From:*Murray Eisenberg <murray@math.umass.edu>