scholarly journals New $ q $-supercongruences arising from a summation of basic hypergeometric series

2021 ◽  
Vol 7 (3) ◽  
pp. 4125-4136
Author(s):  
Chuanan Wei ◽  
◽  
Chun Li ◽  
◽  

<abstract><p>With the help of a summation of basic hypergeometric series, the creative microscoping method recently introduced by Guo and Zudilin, and the Chinese remainder theorem for coprime polynomials, we prove some new $ q $-supercongruences on sums of $ q $-shifted factorials. Especially, we give a $ q $-analogue of a formula due to Liu <sup>[<xref ref-type="bibr" rid="b14">14</xref>]</sup>.</p></abstract>






2018 ◽  
Vol 26 (2) ◽  
pp. 99-111
Author(s):  
Xiaoyuan Wang ◽  
Wenchang Chu

AbstractThe q-derivative operator approach is illustrated by reviewing several typical summation formulae of terminating basic hypergeometric series.



10.37236/1703 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
Michael Schlosser

We present a new matrix inverse with applications in the theory of bilateral basic hypergeometric series. Our matrix inversion result is directly extracted from an instance of Bailey's very-well-poised ${}_6\psi_6$ summation theorem, and involves two infinite matrices which are not lower-triangular. We combine our bilateral matrix inverse with known basic hypergeometric summation theorems to derive, via inverse relations, several new identities for bilateral basic hypergeometric series.



2006 ◽  
Vol 49 (1-2) ◽  
pp. 25-44 ◽  
Author(s):  
CHU Wenchang


2015 ◽  
Vol 171 (4) ◽  
pp. 309-326 ◽  
Author(s):  
Victor J. W. Guo ◽  
Jiang Zeng


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