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>
- Re: Symplify Table