Expansions of averaged truncations of basic hypergeometric series
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- by Michael J. Schlosser and Nian Hong Zhou;
- Proc. Amer. Math. Soc. 152 (2024), 4659-4673
- DOI: https://doi.org/10.1090/proc/16775
- Published electronically: September 20, 2024
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Abstract:
Motivated by recent work of George Andrews and Mircea Merca [J. Combin. Theory Ser. A 119 (2012), pp. 1639–1643] on the expansion of the quotient of the truncation of Euler’s pentagonal number series by the complete series, we provide similar expansion results for averages involving truncations of selected, more general, basic hypergeometric series. In particular, our expansions include new results for averaged truncations of the series appearing in the Jacobi triple product identity, the $q$-Gauß summation, and the very-well-poised ${}_5\phi _5$ summation. We show how special cases of our expansions can be used to recover various existing results. In addition, we establish new inequalities, such as one for a refinement of the number of partitions into three different colors.References
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Bibliographic Information
- Michael J. Schlosser
- Affiliation: Fakultät für Mathematik, Universität Wien Oskar-Morgenstern-Platz 1, A-1090, Vienna, Austria
- MR Author ID: 609064
- ORCID: 0000-0002-2612-2431
- Email: nianhongzhou@outlook.com
- Nian Hong Zhou
- Affiliation: Fakultät für Mathematik, Universität Wien Oskar-Morgenstern-Platz 1, A-1090, Vienna, Austria
- MR Author ID: 1280179
- ORCID: 0000-0003-2889-5312
- Email: michael.schlosser@univie.ac.at
- Received by editor(s): July 20, 2023
- Received by editor(s) in revised form: December 1, 2023, and December 4, 2023
- Published electronically: September 20, 2024
- Additional Notes: The first author was partially, and the second author was fully, supported by Austrian Science Fund FWF 10.55776/P32305.
- Communicated by: Mourad Ismail
- © Copyright 2024 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 152 (2024), 4659-4673
- MSC (2020): Primary 33D15; Secondary 05A15, 05A17, 05A20, 05A30
- DOI: https://doi.org/10.1090/proc/16775
- MathSciNet review: 4802621