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arXiv · 1804.08612

A symmetric formula for hypergeometric series

Chuanan Wei
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Abstract

In terms of Dougall's $_2H_2$ series identity and the series rearrangement method, we establish an interesting symmetric formula for hypergeometric series. Then it is utilized to derive a known nonterminating form of Saalsch\"{u}tz's theorem. Similarly, we also show that Bailey's $_6\psi_6$ series identity implies the nonterminating form of Jackson's $_8\phi_7$ summation formula. Considering the reversibility of the proofs, it is routine to show that Dougall's $_2H_2$ series identity is equivalent to a known nonterminating form of Saalsch\"{u}tz's theorem and Bailey's $_6\psi_6$ series identity is equivalent to the nonterminating form of Jackson's $_8\phi_7$ summation formula.

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Chuanan Wei. 2018-04-23. A symmetric formula for hypergeometric series. https://arxiv.org/abs/1804.08612

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