  This paper investigates the relationships between closed and mixed string
amplitudes at the tree level in string theory. Through the analytic
continuation of complex variables, we establish a factorization of closed
string amplitudes into those involving ($n-2$) open strings and a single closed
string. Expressions for four-, five-, and six-point amplitudes are provided,
along with systematic formulations for $n$ strings. The paper addresses
possible correction terms arising from integration along infinite tubes during
the Wick rotation process. In the field theory limit, the correction terms
become negligible due to being of subleading order.
