The qFunctions package is a Mathematica package for q-series and partition theory applications.


The qFunctions package by Jakob Ablinger and Ali K. Uncu is a Mathematica package for q-series and partition theory applications. This package includes both experimental and symbolic tools. The experimental set of elements includes guessers for q-shift equations and recurrences for given q-series and fitting/finding explicit expressions for sequences of polynomials. This package can symbolically handle formal manipulations on q-differential, q-shift equations and recurrences, such as switching between these forms, finding the greatest common divisor of recurrences, and formal substitutions. Here, we also extend the classical method of the weighted words approach. Moreover, qFunctions has implementations that automate the recurrence system creation of the weighted words approach as well as a scheme on cylindric partitions.

Registration and Legal Notices

The source code for this package is password protected. To get the password send an email to Peter Paule. It will be given for free to all researchers and non-commercial users. Copyright © 2019 The RISC Combinatorics Group, Austria — all rights reserved. Commercial use of the software is prohibited without prior written permission.

A Note on Encoded Files

This package contains one or more Mathematica input files which are encoded. Those files cannot be read or modified directly as plain text, but can be loaded into Mathematica just like any normal input file (i.e., with <<"file" or Get["file"]). There is no need (and also no way) to decode them by using additional software or a special key.

The Package

The package is contained in the Mathematica input file After loading the package, type qFunctionsList to get a description of the available commands. Right now you are using Version 1.0 released on October 24, 2019. This version was tested with Mathematica versions 11.3 and 12.0.


  • qFunctions - A Mathematica package for q-series and partition theory applications. [pdf]


Please report any bugs, comments and requests to Jakob Ablinger or Ali K. Uncu.