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Can anyone explain what's meant by this? > Multiplying by x^(n+2) and summing over all n, we get Is n the iterating variable, or the domain? What are the pos

Can anyone explain what's meant by this? > Multiplying by x^(n+2) and summing over all n, we get Is n the iterating variable, or the domain? What are the possible values of n? Wouldn't "all" values (whichever set that may be) give an infinite sum? I thought that infinite expressions did not obey the same laws as finite ones, and couldn't be generally used with algebraic transformations. I guess I don't know as much math as I thought.

MHordecki 11y ago
Disclaimer: I have studied these functions a long, long time ago. I barely remember anything. In that particular point in the article, n is both. It is a natural number that is the domain of Fib, and the iterating variable of the generating function. As you've noticed, the sum is indeed infinite - this does not matter, however, as at no point is the actual sum of a generating function series important - the whole series mechanism is just a nice conduit to reason about the coefficients (subsequent values of Fib, in this case) using more familiar and developed mathematics for infinite series (divergent or not). I remember being fascinated by generating functions in college. I viewed them as sort of a beautiful hack in how to tie various combinatorial structures to the more ordinary algebraic operations. This mini-field is called enumerative combinatorics. The only part of discrete mathematics that I've actually enjoyed :)