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We discover an infinite number of recurrence relations among Regge stringscattering amplitudes \cite{bosonic,RRsusy} of different string states atarbitrary mass levels in the open bosonic string theory. As a result, all Reggestring scattering amplitudes can be algebraically solved up to multiplicativefactors. Instead of decoupling zero-norm states in the fixed angle regime, thecalculation is based on recurrence relations and addition theorem of Kummerfunctions of the second kind. These recurrence relations among Regge stringscattering amplitudes are dual to linear relations or symmetries amonghigh-energy fixed angle string scattering amplitudes discovered previously.

Recurrence relations of Kummer functions and Regge string scattering amplitudes