Fine’s function and partial theta function
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- by Heng Huat Chan, Song Heng Chan, Kuo-Jye Chen and Sen-Shan Huang PDF
- Proc. Amer. Math. Soc. 149 (2021), 2561-2572 Request permission
Abstract:
In this article, we use identities found in N.J. Fine’s book Basic hypergeometric series and its applications to derive a one-parameter generalization of the product of two partial theta functions discovered by G.E. Andrews and S.O. Warnaar. We also give two different proofs of this generalization, one of which is motivated by the work of A. Berkovich and the other is given by M.E.H. Ismail.References
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Additional Information
- Heng Huat Chan
- Affiliation: Department of Mathematics, National University of Singapore, Singapore 119076, Singapore; Department of Mathematics, National Changhua University of Education, Jin-De Campus, No. 1, Jin-De Road, Changhua City, Taiwan
- MR Author ID: 365568
- Email: matchh@nus.edu.sg
- Song Heng Chan
- Affiliation: Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
- MR Author ID: 730779
- Email: chansh@ntu.edu.sg
- Kuo-Jye Chen
- Affiliation: Department of Mathematics, National Changhua University of Education, Jin-De Campus, No. 1, Jin-De Road, Changhua City, Taiwan
- MR Author ID: 352175
- Email: kjchen@cc.ncue.edu.tw
- Sen-Shan Huang
- Affiliation: Department of Mathematics, National Changhua University of Education, Jin-De Campus, No. 1, Jin-De Road, Changhua City, Taiwan
- MR Author ID: 620036
- Email: sshuang@cc.ncue.edu.tw
- Received by editor(s): October 1, 2020
- Received by editor(s) in revised form: October 8, 2020
- Published electronically: March 29, 2021
- Communicated by: Mourad Ismail
- © Copyright 2021 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 149 (2021), 2561-2572
- MSC (2020): Primary 33D15
- DOI: https://doi.org/10.1090/proc/15380
- MathSciNet review: 4246806
Dedicated: Dedicated to the memory of Professor Richard Askey