Analytic continuations of the Horn H_1 and H_5 functions

The analytic continuations (ACs) of the double variable Horn H_1 and H_5 functions have been derived for the first time using the automated symbolic Mathematica package Olsson.wl. The use of Pfaff–Euler transformations have been emphasised in deriving AC to cover regions which are otherwise not possible. The corresponding regions of convergence (ROC) are obtained using its companion package ROC2.wl. A Mathematica package HornH1H5.wl, containing all the derived ACs and the associated ROCs, along with a demonstration file of the same is made publicly available in this URL: https://github.com/souvik5151/Horn_H1_H5.git .