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