Disclaimer: terminology and syntax may be incorrect as I do not use them often, please excuse the errors.
Function
The function I am trying to convert:
$ f(a,b,c) = \displaystyle\sum_{n=0}^{a} \left( \frac{b}{c} \right)^n$
$ a >= 0$
$ b,c > 0$
$ c > b $
$ b $ and $ c $ are listed as separate parameters as they have to be interchangeable in a possible solution.
Limitations & Thoughts
This function has to be implemented programmatically. But due to system structure limitation this implementation can't use any form of loop or recursion. Thus the summation in the formula can't be implemented.
Testing the function with different value combinations reveals what looks to me like a logarithmic curve.
How can I convert the function above correctly?
That's not a logarithm. The sum of this geometric progression is famously $(1-(b/c)^{a+1})/(1-b/c)$. You can prove this by induction on $a$.