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A symmetric formula for hypergeometric series
The Ramanujan Journal ( IF 0.7 ) Pub Date : 2020-07-16 , DOI: 10.1007/s11139-019-00248-8
Chuanan Wei

In terms of Dougall’s \(_2H_2\) series identity and the series rearrangement method, we establish a symmetric formula for hypergeometric series. Then it is utilized to derive a known nonterminating form of Saalschütz’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 Saalschütz’s theorem and Bailey’s \(_6\psi _6\) series identity is equivalent to the nonterminating form of Jackson’s \(_8\phi _7\) summation formula.



中文翻译:

超几何级数的对称公式

根据Dougall的\(_ 2H_2 \)序列恒等式和序列重排方法,建立了超几何序列的对称公式。然后利用它来推导萨尔舒茨定理的一个已知的非终止形式。同样,我们还表明,贝利的\(_ 6 \ psi _6 \)系列恒等式暗示了杰克逊的\(_ 8 \ phi _7 \)求和公式的非终止形式。考虑到证明的可逆性,通常可以证明道格拉的\(_ 2H_2 \)系列恒等价于Saalschütz定理的已知非终止形式,而贝利的\(_ 6 \ psi _6 \)系列恒等价于杰克逊的\(_ 8 \ phi _7 \)求和公式。

更新日期:2020-07-16
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