Olsson.wl : a Mathematica package for the computation of linear transformations of multivariable hypergeometric functions

12/31/2021

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by   B. Ananthanarayan, et al.

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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) in order to derive the analytic continuations of the Appell F_1 double hypergeometric series from the linear transformations of the Gauss _2F_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. This package can be used independently of Olsson.wl.