I don't have Maple yet, but if it can solve this problem for me then I'm ready to purchase!

I have a probability mass function pmf(i, n) to define a discrete probability distribution, based on a combinatoric analysis of an object of size n. So I don't have a drv X, I have a formula to generate X_n for 0 <= n, where n + 1 is then the size of the outcome alphabet.

In other words, 
X_n = {0 <= i <= n : p(x_i) = pmf(i, n)}

Where pmf(i, n) is 'well behaved' in the sense that it's not producing arbitrary results. As n increases, X_n has the same distribution simply with more detail.

So my question is, can Maple calculate the entropy, usually written H(X), of this distribution at, dare I say it, the limit, X_∞?

Can it calculate it symbolically, or can it 'only' approximate it by a Taylor series or something?

Thanks in advance, this problem really has me stumped!