A formal power series, sometimes simply called a "formal series", of a field F is an infinite sequence {a_0, a_1, a_2, ...} over F. Equivalently, it is a function from the set of nonnegative integers to F, {0, 1, 2, ...}->F. A formal power series is often written a_0 + a_1 x + a_2 x^2 + ... + a_n x^n + ..., but with the understanding that no value is assigned to the symbol x.
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