Factorial Basis Method for q-Series Applications: To the memory of an inspirational mathematician, Marko Petkovšek

Antonio Jiménez-Pastor, Ali Kemal Uncu

Research output: Chapter or section in a book/report/conference proceedingChapter in a published conference proceeding

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.

Original languageEnglish
Title of host publicationISSAC 2024 - Proceedings of the 2024 International Symposium on Symbolic and Algebraic Computation
EditorsShaoshi Chen
Place of PublicationNew York, U. S. A
PublisherAssociation for Computing Machinery
Pages382-390
Number of pages9
ISBN (Electronic)9798400706967
DOIs
Publication statusPublished - 16 Jul 2024
Event49th International Symposium on Symbolic and Algebraic Computation, ISSAC 2024 - Raleigh, USA United States
Duration: 16 Jul 202419 Jul 2024

Publication series

NameProceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC
ISSN (Electronic)1532-1029

Conference

Conference49th International Symposium on Symbolic and Algebraic Computation, ISSAC 2024
Country/TerritoryUSA United States
CityRaleigh
Period16/07/2419/07/24

Funding

The authors would like to thank the anonymous referees for their encouragement and their invaluable comments that made this paper's exposition better. The first author was partially supported by the Poul Due Jensen Grant 883901. The second author acknowledges the EPSRC grant number EP/T015713/1 and the FWF grant P-34501N for partially supporting his research.

FundersFunder number
Austrian Science Fund
EPSRC Centre for Doctoral Training in Cyber SecurityEP/T015713/1

    Keywords

    • definite hypergeometric sums
    • holonomic
    • integer partitions
    • q-series
    • shift-compatible factorial bases

    ASJC Scopus subject areas

    • General Mathematics

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