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We review and extend high energy string BCJ relations in both the fixed angleand Regge regimes. We then give an explicit proof of four point string BCJrelations for all energy. This calculation provides an alternative proof of theone based on monodromy of integration in string amplitude calculation. Inaddition, we calculate both s-t and t-u channel nonrelativistic low energystring scattering amplitudes of three tachyons and one leading trojectorystring state at arbitrary mass levels. We discover that the mass and spindependent nonrelativistic string BCJ relations can be expressed in terms ofGauss hypergeometry functions. As an application, for each fixed mass level N,we derive extended recurrence relations among nonrelativistic low energy stringscattering amplitudes of string states with different spins and differentchannels.

The String BCJ Relations Revisited and Extended Recurrence relations of Nonrelativistic String Scattering Amplitudes