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MathGroup Archive 2001

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Re: Assumptions question (1/m^x,x>1,m=Infinity)

  • To: mathgroup at smc.vnet.net
  • Subject: [mg31056] Re: [mg31041] Assumptions question (1/m^x,x>1,m=Infinity)
  • From: Andrzej Kozlowski <andrzej at bekkoame.ne.jp>
  • Date: Sat, 6 Oct 2001 03:32:26 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Simplify with assumptions relies on an algebraic mechanism and with a 
few exceptions it will not work with non-algebraic expressions. In 
particular it will have no effect on Limit. Nor can you use any 
assumptions inside Limit (though both Limit and Integrate will sometime 
make silent assumptions about the variables, which may or may not be the 
ones you wish them to make).

Still, there are several possible ways to deal with some problems of 
this kind. However, the example you give is just too trivial to serve as 
a good illustration and actually ought to be done by hand. Still, here 
is one way one could try to use Mathematica to solve this sort of 
problem. Unfortunately it is not guaranteed to work in other cases, 
since Integrate with Assumptions on which it depends on is very erratic.

Observe that:

In[1]:=
D[m^-x,m]

Out[1]=
(-m^(-1 - x))*x

This means that

In[2]:=
Integrate[(-m^(-1 - x))*x, {m, 1, Infinity},
     Assumptions -> {Re[x] > 1}] + Integrate[(-m^(-1 - x))*x,
     m] /. m -> 1

Out[2]=
0

must be the result you wanted.

There are other ways, but you would have to present your real problem 
first.

Andrzej Kozlowski
Toyama International University
JAPAN
http://platon.c.u-tokyo.ac.jp/andrzej/



On Friday, October 5, 2001, at 02:22  PM, Hugo Buddelmeijer wrote:

> How do I simplify this:
> 1/m^x
> when I know that x>1 and m is extremely large, so this term cancels
> and becomes 0.
> I'm thinking about something like:
> Simplify[Limit[1/m^x,m->Infinity],x>1]
> But I can't get math to figure out what I meant, I've tried about all
> possible things with Simplify, Limit and Assumptions that I've realy
> run out of ideas..
> I'm realy desperate... BTW, I'm using mathematica 4.1 for linux.
> Any help would be very much appreciated,
> groetjes,
> Hugo
>
>
>



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