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Abstract
Assumed A is infinitesimal generator of C0-semigroup T(t) on X. This could be defined as T(t)=etA, applies if A is a bounded linear operator. Not if A is unbounded linear operator, then it will result in one possibility that show T(t) could be represented as etA. This paper will discuss and detail the proof of the other two formulas that show T(t) could be represented as etA.