I'm given an expression
$A\ T^a+B\ T^{-b},$ $\text{with} \ \ \ \ A,B>0,\ \ \ \ a,b\in(0,1),$
but the plus sign "$+$" is a problem for my purposes. I want to make a fit of the following form:
$C\ T^c\exp{(\small{-\frac d T})}.$
The approximation should take the closest values to the original function in an interval from $T_1$ to $T_2$, both positive. The term $A\ T^a$ clearly dominates the original expression for big $T$, as well as $C\ T^c$ when the exponential gets turned off. Regardless of that, the point is that I'd have an idea to do this in a neighborhood around a point, but here I'm convened with a whole interval, especially the values after $T_1$.
What is the general theory for this?
And specifically, I'd like to know how to do this in Mathematica.