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arXiv · 2210.17370

Analytic continuations of the Horn $H_1$ and $H_5$ functions

Souvik Bera·Tanay Pathak
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Abstract

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 $\textit{Mathematica}$ package $\texttt{Olsson.wl}$. The use of Pfaff-Euler transformations have been emphasised to derive AC to cover regions which are otherwise not possible. The corresponding region of convergence (ROC) is obtained using its companion package $\texttt{ROC2.wl}$. A $\textit{Mathematica}$ package $\texttt{HornH1H5.wl}$, containing all the derived ACs and the associated ROCs, along with a demonstration file of the same is made publicly available in https://github.com/souvik5151/Horn_H1_H5 .

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Souvik Bera, Tanay Pathak. 2022-10-31. Analytic continuations of the Horn $H_1$ and $H_5$ functions. https://doi.org/10.1140/epjs%2Fs11734-023-00990-7

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