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1. Formal series over a commutative field
1.1 Definitions and general information
A formal series on a commutative field K can intuitively be seen as a kind of infinite polynomial, and operations on polynomials can be generalized within this framework. Of course, not all possible operations are necessarily generalizable: we can't always calculate the composite of two formal series; we must also be careful not to "specialize" without precaution, i.e. to give the traditional "indeterminate X" of polynomials any value taken from the field K.
Definition 1: Let K be a commutative field. Any expression of the type
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