Appell and Lauricella Saran Functions

This repository contains four Mathematica packages: AppellF1.wl, AppellF3.wl, LauricellaFD.wl and LauricellaSaranFS.wl. These can be used to find the numerical values of the Appell $F_1$, $F_3$, Lauricella $F_D^{(3)}$ and Lauricella-Saran $F_S^{(3)}$ functions for real values of variables. The work is based on the following work:

Analytic continuations and numerical evaluation of Appell $F_1$, $F_3$, Lauricella $F_D^{(3)}$ and Lauricella-Saran $F_S^{(3)}$.

Installation

After setting the path, the packages can be called using the following command. We only show the demonstration for AppellF1.wl package. All the other packages have similar commands.

<<AppellF1.wl

This package has the following five commands:

1. F1
2. F1findall
3. F1expose
4. F1evaluate
5. F1ROC

To be noted that the last command and F3ROC are only available in AppellF1.wl and AppellF3.wl packages respectively.

A detailed demonstration of the packages is presented in the paper.

The repository, along with the packages, also contains various test files used for the testing of the packages via various other means.