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

@article{Michel2008FastCO,
  title={Fast computation of the Gauss hypergeometric function with all its parameters complex with application to the P{\"o}schl-Teller-Ginocchio potential wave functions},
  author={N. Michel and M. V. Stoitsov},
  journal={Computer Physics Communications},
  year={2008},
  volume={178},
  pages={535-551}
}
The fast computation of the Gauss hypergeometric function 2F1 with all its parameters complex is a difficult task. Although the 2F1 function 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 are inaccessible using only 2F1 power series formulas, thus rendering 2F1 evaluations impossible on a… CONTINUE READING