  We discover that the 26D open bosonic string scattering amplitudes (SSA) of
three tachyons and one arbitrary string state can be expressed in terms of the
D-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 various
limits calculated previously can be rederived. These include the linear
relations conjectured by Gross [1-3] and proved in [4-9] in the hard scattering
limit, the recurrence relations in the Regge scattering limit [14-16] and the
extended recurrence relations in the nonrelativistic scattering limit [19]
discovered recently. Finally, as an application, we calculate a new recurrence
relation of SSA which is valid for all energies.
