# Fast computation of the Gauss hypergeometric function with all its parameters complex with application to the Pöschl–Teller–Ginocchio potential wave functions

## Description

Abstract The fast computation of the Gauss hypergeometric function _2 F_1with all its parameters complex is a difficult task. Although the _2 F_1function verifies numerous analytical properties involving power series expansions whose implementation is apparently immediate, their use is thwarted by instabilities induced by cancellations between very large terms. Furthermore, small areas of the complex plane, in the vicinity of z = e^(± i frac(π, 3)), are inaccessible using _2 F_1power series li... Title of program: hyp_2F1, PTG_wf Catalogue Id: AEAE_v1_0 Nature of problem The Gauss hypergeometric function 2 F 1 , with all its parameters complex, is uniquely calculated in the frame of transformation theory with power series summations, thus providing a very fast algorithm. The evaluation of the wave functions of the analytical Pöschl-Teller-Ginocchio potential is treated as a physical application. Versions of this program held in the CPC repository in Mendeley Data AEAE_v1_0; hyp_2F1, PTG_wf; 10.1016/j.cpc.2007.11.007 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)