  We calculate explicitly residues of all n-point Koba-Nielsen (KN) amplitudes
by using on-shell recursion relation of string scattering amplitudes (SSA). In
addition, we show that the residues of all SSA including the KN amplitudes can
be expressed in terms of the Lauricella functions. This result demonstrates the
exact SL(K+3,C) symmetry of the tree-level open bosonic string theory.
Moreover, we derive an iteration relation among the residues of a given SSA.
This iteration relation is related to the SL(K+3,C) symmetry and can presumably
be used to soften the well-known hard SSA.
