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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: [mg31077] Re: Assumptions question (1/m^x,x>1,m=Infinity)
  • From: hugo at doemaarwat.nl (BlackShift)
  • Date: Sun, 7 Oct 2001 03:11:42 -0400 (EDT)
  • Organization: Rijksuniversiteit Groningen
  • References: <9pmdb3$62v$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

On Sat, 6 Oct 2001 07:54:11 +0000 (UTC), Andrzej Kozlowski
<andrzej at bekkoame.ne.jp> wrotf:

>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 

Can do it by hand of course, but since the formula's got quite large
at the moment I wanted to make the substitution it wasn't that easy to
do by hand...

>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[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.

Hmm, that's actually quite true, I get that formula by integration, so
I can use the assumption there already (why didn't I think of that).
Nonetheless, isn't it possible to do it afterwards? That would be a
'nicer' thing to do, since it is part of a model, where m doesn't have
to be Infity in all cases

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

I think I can make mathematica do what I want now, but if you know a
method to make the assumption that m is infinity later on in the
calculations that would be very great, so here is the real problem

(x=x, MU=m)
Background: It is a model of starforming in galaxies,
Phi[M_]dM is the ratio of stars formed with a mass between M and M+dM
x is just a parameter for the model

In[1]:= Phi[M_]=Cp*M^(-1-x)

To normalize Cp (which is just a normalization factor) I Integrate
over al possible M, from ML (lower mass, about .1 solar masses) to MU
(upper mass, about 32 solar masses)

In[2]:= subC=Solve[Integrate[Phi[M],{M,ML,MU}]==1,Cp][[1]]
                     1
Out[2]= {Cp -> -------------}
                 1       1
               ----- - -----
                 x       x
               ML  x   MU  x

with which I calculate further, with Cp in the expresions, in the
final result /.subC them. In some cases it is better to choose for ML
and MU the numbers 0.1 and 32, but sometimes it is algebraically
easyer to assume ML->0 or MU->Infinity, so sometimes I want to do
/.subC/.{ML->0.1,MU->32}, and sometimes
/.subC/.{ML->0.1,MU->Infinity}, depending on the equations, but the
latter isn't possible:

In[4]:= subC/.{ML->0.1,MU->Infinity}

Out[4]= {Cp -> Indeterminate}

Because it is indeterminate when x=0, which is not the case (x~1.3).

Is there anyway I can do this? without explicitly giving a value for
x, since that is the last valuable to enter (so I can test what value
for x is likely)

BTW, why doesn't mathematica not result with an If statement which
says that it is only indeterminate when x=0 and give Cp->0 otherwise.
That would be more logical behavoir I think.

groetjes,
hugo


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