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We discover that the 26D open bosonic string scattering amplitudes (SSA) ofthree tachyons and one arbitrary string state can be expressed in terms of theD-type Lauricella functions with associated SL(K+3,C) symmetry. As a result,SSA and symmetries or relations among SSA of different string states at variouslimits calculated previously can be rederived. These include the linearrelations conjectured by Gross [1-3] and proved in [4-9] in the hard scatteringlimit, the recurrence relations in the Regge scattering limit [14-16] and theextended recurrence relations in the nonrelativistic scattering limit [19]discovered recently. Finally, as an application, we calculate a new recurrencerelation of SSA which is valid for all energies.

The Exact SL(K+3,C) Symmetry of String Scattering Amplitudes