ABSTRACT
Power series The use of generating functions is one way of book-keeping. Let a : Z+ → C be any function, in other words, a sequence an of complex numbers. Then one associates to it the power series
∑ anx
n. The power series may not converge anywhere except x = 0, that is to say, its radius of convergence may be 0. If b is another such sequence, then the product of the two power series is associated to the function n → ∑i=ni=0 aibn−i. This is the Cauchy product of two sequences and so already we notice that associating the power series to the sequence has some advantage.
