Recurrence relations of Kummer functions and Regge string scattering amplitudes

Understand

We discover an infinite number of recurrence relations among Regge string scattering amplitudes \cite{bosonic,RRsusy} of different string states at arbitrary mass levels in the open bosonic string theory.

• As a result, all Regge string scattering amplitudes can be algebraically solved up to multiplicative factors.
• Instead of decoupling zero-norm states in the fixed angle regime, the calculation is based on recurrence relations and addition theorem of Kummer functions of the second kind.
• These recurrence relations among Regge string scattering amplitudes are dual to linear relations or symmetries among high-energy fixed angle string scattering amplitudes discovered previously.