Kummer function and High energy String Scatterings

Based on a summation algorithm for Stirling number identity developed recently, we discover that the ratios calculated previously among high energy string scattering amplitudes in the Gross regime (GR) can be extracted from the Kummer function of the second kind. This function naturally shows up in the leading order of high energy string scattering amplitudes in the Regge regime (RR). As a result, the identity suggested by string theory calculation can be rigorously proved by a totally different but sophisticated mathematical method. We conjecture and give evidences that the existence of these ratios in the RR persists to all orders in the Regge expansion of high energy string scattering amplitudes.