An equivalency of Bailey’s very-well-poised ₆𝜓₆ summation and Weierstrass’ theta function identity

Wang, Jin; Ma, Xinrong

doi:10.1090/proc/14438

An equivalency of Bailey’s very-well-poised $_6\psi _6$ summation and Weierstrass’ theta function identity
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Proc. Amer. Math. Soc. 147 (2019), 2953-2961 Request permission

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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