  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 first conjectured by Gross [1-3] and later corrected and proved in
[4-9] in the hard scattering limit, the recurrence relations in the Regge
scattering limit with associated SL(5,C) symmetry [19-21] and the extended
recurrence relations in the nonrelativistic scattering limit with associated
SL(4,C) symmetry [24] discovered recently. Finally, as an application, we
calculate a new recurrence relation of SSA which is valid for all energies.
