where,
H is the hash rate in GH/s
D is the difficulty when mining starts
R is the rate of increase at every difficulty adjustment (e.g. 20% = 0.2)
Do you know the integral expression used to obtain this formula? One which doesn't require strictly exponential difficulty scaling and leaves R and D as general functions?
The revenue is simply the sum of the cumulative payouts for each difficulty period. Assuming constant exponential growth turns it into a power series which has a simple formula. In reality, the formula above is a simplification, because the revenue for each period also depends on the average hashing power for the period (which also affects length of the period and the next difficulty value). I suspect the formula should be "... * R / (1+R)" instead of "... / R"