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Other Examples: A rational function is the ratio of two polynomials P(x) and Q(x) like this. Except that Q(x) cannot be zero (and anywhere that Q(x)=0 is undefined) A root (or zero) is where the expression is equal to zero:
Every function which has derivatives of all orders at 0 is the generating function of its Taylor expansion at 0. > 1/(1-x)=series(1/(1-x),x,20); Uses of generating functions. One use for generating functions is get closed formulas for sequences which are defined recursively in terms of previous terms. The defining equations for such sequences are called recurence relations.