Olsson.wl: A Mathematica Package for the Computation of Linear Transformations of Multivariable Hypergeometric Functions

We present the Olsson.wl Mathematica package which aims to find linear transformations for some classes of multivariable hypergeometric functions. It is based on a well-known method developed by P. O. M. Olsson in J. Math. Phys. 5, 420 (1964) to derive the analytic continuations of the Appell \(F_{1}\) double hypergeometric series from the linear transformations of the \(\text {Gauss }_{2}F_{1}\) hypergeometric function. We provide a brief description of Olsson’s method and demonstrate the commands of the package, along with examples. We also provide a companion package, called ROC2.wl and dedicated to the derivation of the regions of convergence of double hypergeometric series. As applications, we show the usefulness of the package in finding the analytic continuations of Feynman integrals via their hypergeometric function representation.