st: Doing something an observation-specific number of times

[robert hartman <rohartman@gmail.com>]

Hi Listers,
Imagine that observation 1 has v1 and v2 values of .41 and 78,
respectively. There are many other observations like this, where v1
values lie on the unit interval and v2 values are positive integers
(let's say the upper bounded is 600). I want to create a new variable
and store in it the results of an algebraic equation that uses the v1
and v2 values from same row, as well as some constants, and where
"observation-specific exponentiation" is happening. For example, let's
say I want to add a constant to v1 raised to some power and then
divide that by some other constant. And let's say that the "some
power" is  every power from 1 to the v2 value inclusive (e.g., 1
through 78 in this case, 1 through 2 if the v2 value is 2...) and then
sum up those terms.  For example, for observation 1, the new obs 1 v3
value=((1+(.41^1))/2) + ((1+(.41^2))/2) ...((1+(.41^77))/2) +
((1+(.41^78))/2). The specific use case is convoluted, and I don't
think in-depth understanding of it is critical to the programming
(we'll see).

I have begun to think of some klugy ways of doing this via looping or
even the expand command. However, whereas my Stata programming skills
are mediocre and have been acquired ad hoc, I thought some of you
might have some insights as to a relatively computationally efficient
and/or lines-of-code efficient way of doing this kind of thing. There
may even be some kind of obvious (to you, not me) algebraic workaround
that I'm not catching.

Thanks,
Rob
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