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

dataset

posted on 06.12.2019 by N. Michel, M.V. Stoitsov#### dataset

Datasets usually provide raw data for analysis. This raw data often comes in spreadsheet form, but can be any collection of data, on which analysis can be performed.

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)