Factorial Basis Method for q-Series Applications
<|reference_start|>Factorial Basis Method for q-Series Applications: The Factorial Basis method, initially designed for quasi-triangular, shift-compatible factorial bases, provides solutions to linear recurrence equations in the form of definite-sums. This paper extends the Factorial Basis method to its q-analog, enabling its application in q-calculus. We demonstrate the adaptation of the method to q-sequences and its utility in the realm of q-combinatorics. The extended technique is employed to automatically prove established identities and unveil novel ones, particularly some associated with the Rogers-Ramanujan identities.<|reference_end|>
@article{jiménez-pastor2024factorial,
    title={Factorial Basis Method for q-Series Applications},
    author={Antonio Jim'enez-Pastor and Ali Kemal Uncu},
    journal={arXiv preprint arXiv:2402.04392},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.04392},
    primaryClass={cs.SC math.CO}
}