A bug in Integrate?
- To: mathgroup at smc.vnet.net
- Subject: [mg22810] A bug in Integrate?
- From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
- Date: Fri, 31 Mar 2000 01:01:13 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
While replying to another posting (Re: [mg22760] Got a trouble with the
Limit[]) I was trying to think of a way to get Mathematica to effectively
tell us that Lim[a^-x,x->Infinity] is 0 if a>1. One indirect way to do this
is to make Mathematica evaluate
Integrate[Log[a]*a^x, {x, 1, Infinity}, Assumptions -> {Im[a] == 0}] +
Integrate[Log[a]*a^x, x] /. x -> 1
I was expecting to get an answer of the form If[a>1,...] but this is what
happened:
In[1]:=
Integrate[Log[a]*a^x, {x, 1, Infinity}, Assumptions -> {Im[a] == 0}] +
Integrate[Log[a]*a^x, x] /. x -> 1
Out[1]=
0
This looks like a bug to me (rather than Mathematica deliberately choosing
only to consider the case when the integral exists) particularly if you
compare it with:
In[2]:=
Integrate[x^a, {x, 1, Infinity}, Assumptions -> {Im[a] == 0}]
Out[2]=
1 a
If[a < -1, ------, Integrate[x , {x, 1, Infinity}]]
-a - 1
--
Andrzej Kozlowski
Toyama International University
Toyama, Japan
http://sigma.tuins.ac.jp/