MBCHProcess

A Mathematica package for post-processing Mellin-Barnes (MB) representations evaluation generated by MBConicHulls by identifying and expressing series as known generalized hypergeometric functions (HypergeometricPFQ, AppellF1, Horn, Lauricella A/B/C/D, and Kampe de Feriet).

Prerequisites

• Wolfram Mathematica (12.0 or later recommended).
• The MBConicHulls package must be installed and loaded before MBCHProcess, as it relies on MBConicHullsEvaluateSeries`.

Installation

Place the MBCHProcess.m file in Mathematica's $UserBaseDirectory/Applications folder.

Usage

Load the package (ensure MBConicHulls is loaded first):

Needs["MBConicHulls`"];
Needs["MBCHProcess`"];

Process a resolved MB representation using the ProcessSeries function:

ProcessSeries[rep, n, Evaluate :> False, Verbose -> False]

Arguments and Options:

• rep: The resolved MB representation (result of ResolveMB from MBConicHulls).
• n: The series index to process.
• Evaluate: If True, returns the result in InputForm for numerical evaluation.
• Verbose: If True, prints intermediate algebraic simplification steps.

Methodology

The package sequentially applies algebraic transformations to the series general term:

1. Factorizes Gamma arguments and applies the Gauss multiplication formula.
2. Uses the reflection formula to normalize summation indices to positive signs.
3. Converts Gamma functions to Pochhammer symbols.
4. Analyzes the index structure to map the series to standard special functions.

Authors

Yanis Seyifou, Quentin Urzel and Ewen Mahé (supervised by Dr. Samuel Friot, IJCLab, Orsay, France).

License

This project is licensed under the MIT License.