On a generalized Weierstrass theta identity
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- by Jin Wang PDF
- Proc. Amer. Math. Soc. 150 (2022), 719-730 Request permission
Abstract:
The classical Weierstrass theta identity plays a central role in the study of modular, elliptic and theta hypergeometric series. In this paper, we establish a multi-parameter Weierstrass theta identity with the use of the Cauchy determinant and an anti-symmetric difference of a product of two theta functions. Some applications of this generalized Weierstrass theta identity to basic and elliptic hypergeometric series are also discussed.References
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Additional Information
- Jin Wang
- Affiliation: Department of Mathematics, Zhejiang Normal University, Jinhua 321004, People’s Republic of China
- MR Author ID: 1180622
- Email: jinwang@zjnu.edu.cn
- Received by editor(s): February 21, 2021
- Received by editor(s) in revised form: May 18, 2021
- Published electronically: November 19, 2021
- Additional Notes: This work was supported by the Natural Science Foundation of Zhejiang Province (Grant No. LQ20A010004) and the National Natural Science Foundation of China (Grant No. 12001492 and  11971341)
- Communicated by: Mourad Ismail
- © Copyright 2021 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 150 (2022), 719-730
- MSC (2020): Primary 33D90; Secondary 33D15, 33E05
- DOI: https://doi.org/10.1090/proc/15685
- MathSciNet review: 4356182