  In this paper, we present a systematic derivation aimed at obtaining general
expressions for on-shell recursion relations for tree-level open string
amplitudes. Our approach involves applying the BCFW shift to an open string
amplitude written in terms of multiple Gaussian hypergeometric functions. By
employing binomial expansions, we demonstrate that the shifted amplitudes
manifest simple poles, which correspond to scattering channels of intermediate
states. Using the residue theorem, we thereby derive a general expression for
these relations.
