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An equivalency of Bailey's very-well-poised $ _6\psi_6$ summation and Weierstrass' theta function identity


Authors: Jin Wang and Xinrong Ma
Journal: Proc. Amer. Math. Soc. 147 (2019), 2953-2961
MSC (2010): Primary 33D15; Secondary 33C45
DOI: https://doi.org/10.1090/proc/14438
Published electronically: March 15, 2019
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Abstract: In the present paper, by establishing a general transformation via the use of some basic transformations for $ {}_8\phi _7$ series, we show certain equivalency of Bailey's fundamental summation formula for bilateral very-well-poised $ _6\psi _6$ series and Weierstrass' theta function identity.


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Additional Information

Jin Wang
Affiliation: Department of Mathematics, Soochow University, Suzhou 215006, People’s Republic of China
Email: jinwang2016@yahoo.com

Xinrong Ma
Affiliation: Department of Mathematics, Soochow University, Suzhou 215006, People’s Republic of China
Email: xrma@suda.edu.cn

DOI: https://doi.org/10.1090/proc/14438
Keywords: Basic hypergeometric series, very-well-poised, Bailey's $_6\psi_6$ summation, Rogers' $_6\phi_5$ summation, Weierstrass' theta function identity, triple product identity, symmetric transformation
Received by editor(s): September 30, 2018
Received by editor(s) in revised form: October 6, 2018
Published electronically: March 15, 2019
Additional Notes: The second author was supported by NSF of China (Grant No. 11471237). The second author is the corresponding author.
Communicated by: Mourad E. H. Ismail
Article copyright: © Copyright 2019 American Mathematical Society