This paper introduces HyperPrecision, a Mathematica package that computes high‑precision numerical values of multivariate hypergeometric functions and their Laurent (epsilon) expansions. These multivariable functions are common in physics and mathematics, but they are usually defined by infinite series that only converge in small regions. That makes it hard to get reliable numerical values far from the series’ region of convergence.

The authors’ approach is to turn the multivariable problem into a one‑dimensional differential equation. From the series definition of a Horn‑type hypergeometric function, the package automatically builds the associated Pfaffian system — a set of partial differential equations that the function satisfies. It then restricts that system to a straight line in the space of variables between a known starting point (the origin) and the target point. That restriction gives an ordinary differential equation, which HyperPrecision solves numerically using the Frobenius method. The starting values at the origin are fixed analytically from the defining series, so no extra numerical input is needed. To obtain the Laurent expansion in a small parameter ε, the package computes values on a grid of ε values and reconstructs expansion coefficients by interpolation.

The implementation is written for Wolfram Mathematica (version 12.3 or higher) and is published under the GNU General Public License v3. It uses two external components: FiniteFlow to compute the algebraic connection matrices and DESolver (part of AMFlow) to integrate the resulting ordinary differential equations. The package name and entry point are HyperPrecision.wl (version 1.0), and a developer repository is given (github.com/HyperPrecision/HyperPrecision).

The authors illustrate and validate the package on many familiar multivariate families. Examples include the Appell functions F1, F2, F3, F4, Horn G and H series, and the Lauricella functions FA, FB, FC, and FD. They also report tests on physics examples such as one‑loop bubble and two‑loop sunset Feynman integrals, angular integrals, and cosmological and holographic correlators. The paper states that the package can, in most cases, evaluate functions at points that lie on singular curves — situations that are especially challenging for direct series evaluation.