A Fast Algorithm for Solving a Kind of Gauss Hypergeometric Functions in Wireless Communication Based on Pfaff Transformation

In order to welcome the arrival of 5G era, many researchers devote themselves to the research work in the field of wireless communication. In this context, basic mathematical research related to this field has become particularly important. Many studies have shown that the evaluating of Gauss hypergeometric function 2_F_1 (1; x; 1 + x; -y) is involved in various communication models, and applied to solve various physical quantities such as signal coverage, connection probability, outage probability, so it is a key basic mathematical problem in this field. Research on this problem not only has a positive effect on related research work in the field of wireless communication, but also promotes the development of interdisciplinary research between wireless communication technology and basic mathematics. Therefore, we proposed a efficient algorithm FPT(Fast Pfaff Transformation algorithm) to solve this problem and conducted a rigorous theoretical analysis of the convergence of the algorithms. Experiments show that the proposed algorithm achieves more than 1000 times the general solution algorithm in terms of solution efficiency, the performance improvement is very significant.