qFunctions – A Mathematica package for q-series and partition theory applications

Abstract

We describe the qFunctions 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-difference equations and recurrences for given q-difference and fitting/finding explicit expressions for sequences of polynomials. This package can symbolically handle formal manipulations on q-differential, q-difference equations and recurrences, such as switching between these forms, finding the greatest common divisor of recurrences, and formal substitutions. The package qFunctions has implementations that automate the recurrence system creation of the weighted words approach as well as a scheme on cylindric partitions. We also discuss a slight extension of the classical method of weighed words and present some new sum-product identities.