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By using on-shell recursion relation of string scattering amplitudes (SSA),we show that all n-point SSA of the open bosonic string theory can be expressedin terms of the Lauricella functions. This result extends the previous exactSL(K+3,C) symmetry of the 4-point Lauricella SSA (LSSA) of three tachyons andone arbitrary string states to the whole tree-level open bosonic string theory.Moreover, we present three applications of the SL(K+3,C) symmetry on the SSA.They are the solvability of all SSA in terms of one amplitude, the existence ofiteration relations among residues of a given SSA so as to soften its hardscattering behavior and finally the re-derivation of infinite linear relationsamong hard SSA [12].

The exact SL(K+3,C) symmetry of string theory