Bibasic Summation, Transformation and Expansion Formulas, q-Analogues of Clausen’s Formula, and Nonnegative Basic Hypergeometric Series

1989 ◽  
pp. 15-34 ◽  
Author(s):  
George Gasper
Keyword(s):  
Hypergeometric Series ◽  
Basic Hypergeometric Series

scholarly journals Approach of q-Derivative Operators to Terminating q-Series Formulae

2018 ◽  
Vol 26 (2) ◽  
pp. 99-111
Author(s):  
Xiaoyuan Wang ◽  
Wenchang Chu
Keyword(s):  
Hypergeometric Series ◽  
Basic Hypergeometric Series ◽  
Operator Approach ◽  
Derivative Operator ◽  
Summation Formulae

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

scholarly journals Inversion of Bilateral Basic Hypergeometric Series

10.37236/1703 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
Michael Schlosser
Keyword(s):  
Hypergeometric Series ◽  
Basic Hypergeometric Series ◽  
Matrix Inversion ◽  
Infinite Matrices ◽  
Inversion Result ◽  
Matrix Inverse ◽  
Bilateral Basic Hypergeometric Series ◽  
Summation Theorem ◽  
Lower Triangular

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.

Some q-supercongruences for truncated basic hypergeometric series

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