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arXiv · 2402.04392

Factorial Basis Method for q-Series Applications

Antonio Jiménez-Pastor·Ali Kemal Uncu
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Abstract

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.

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BibTeXRIS

Antonio Jiménez-Pastor, Ali Kemal Uncu. 2024-02-06. Factorial Basis Method for q-Series Applications. https://arxiv.org/abs/2402.04392

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