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MathGroup Archive 1995

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Restrictions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg2312] Restrictions
  • From: lmedina at leland.Stanford.EDU (Luis Fernando Medina)
  • Date: Mon, 23 Oct 1995 12:44:22 -0400
  • Organization: Stanford University, CA 94305, USA

I have a question that, easy as it may seem, has kept me baffled for 2 days.
If somebody can help me with it, it would be deeply appreciated.

I'm just a beginner in Mathematica and this might be the reason of my troubles.

I'm trying to solve an equation in which the variable I want to solve for
appears as the limit of an integral. However, the integrand is defined in
terms of another variable (more exactly, what I want to do is:
Integrate[y^z, {y, 0, x}]). Mathematica has no problem with this when z is
a given number. However, when z is taken as a variable, mathematica starts to
get fussy with the fact that when y=0, z=-1 the integral is Indeterminate.
I appreciate this mathematical scruples but at this time I don't care because
the way my equation is set up, z is by definition positive. So. all this
boils down to the following: how can I convince Mathematica that z is positive?

Let me tell you some things that I already know that don't work:

i. Defining a w=Abs[z] and then rewrite the original function with w instead of
with z.
ii. Defining a function f[z_] = z for z>0 and then use this new function.

I can substitute for the solution (viz. y^(z+1)/z+1) and then evaluate this
at the boundaries. But that's not what I want because I also want to deal with
other integrals like this that cannot be solved in close form so that, at a
later stage, I can get Mathematica to evaluate them over z. So this type
of suggestion, tempting as it might be, doesn't work neither.

Summing up, I need to find a way to impose some non-negativity restriction
over a variable. This, that looks like very easy, hasn't been so. I must
confess that I'm really surprised that Mathematica cannot do this in a
straightforward way.

That's all by now. I will be extremely grateful I somebody can help me.

Thanks

Luis Fernando Medina.

P.S.: In order not to overload the Net, you can answer to my email:
lmedina at leland.stanford.edu


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