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A Mathematica package for \(q\)-holonomic sequences and power series. (English) Zbl 1180.33030
Summary: We describe a Mathematica package for dealing with \(q\)-holonomic sequences and power series. The package is intended as a \(q\)-analogue of the Maple package gfun and the Mathematica package GeneratingFunctions. It provides commands for addition, multiplication, and substitution of these objects, for converting between various representations (\(q\)-differential equations, \(q\)-recurrence equations, \(q\)-shift equations), for computing sequence terms and power series coefficients, and for guessing recurrence equations given initial terms of a sequence.

MSC:
33F10 Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.)
05A30 \(q\)-calculus and related topics
11B65 Binomial coefficients; factorials; \(q\)-identities
39A10 Additive difference equations
68N30 Mathematical aspects of software engineering (specification, verification, metrics, requirements, etc.)
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