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A new elliptic interpolation formula via the $ (f,g)$-inversion


Author: Jin Wang
Journal: Proc. Amer. Math. Soc. 148 (2020), 3457-3471
MSC (2010): Primary 33D15; Secondary 33E05, 41A05
DOI: https://doi.org/10.1090/proc/15043
Published electronically: March 25, 2020
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Abstract: In the present paper, we establish an elliptic interpolation formula with the help of the $ (f,g)$-inversion formula. As applications, some basic theta function identities are presented, including an equivalent algebraic form of Weierstrass' theta identity.


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Additional Information

Jin Wang
Affiliation: Department of Mathematics, Zhejiang Normal University, Jinhua 321004, Peoples Republic of China
Email: jinwang@zjnu.edu.cn

DOI: https://doi.org/10.1090/proc/15043
Keywords: $q$-series, theta function, triple product identity, interpolation, $(f,g)$-inversion, symmetric difference, Weierstrass' theta identity
Received by editor(s): November 9, 2019
Received by editor(s) in revised form: November 10, 2019, and January 2, 2020
Published electronically: March 25, 2020
Additional Notes: This work was supported by NSF of Zhejiang Province (Grant No. LQ20A010004) and partially by NSF of China (Grant No. 11971341)
Communicated by: Mourad E. H. Ismail
Article copyright: © Copyright 2020 American Mathematical Society