ON THE ANALOGUE OF DIXON'S THEOREM FOR BILATERAL BASIC HYPERGEOMETRIC SERIES

1950 ◽  
Vol 1 (1) ◽  
pp. 318-320 ◽  
Author(s):  
W. N. BAILEY
Keyword(s):  
Hypergeometric Series ◽  
Basic Hypergeometric Series ◽  
Bilateral 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.

scholarly journals Bilateral Basic Hypergeometric Series: A Study

2018 ◽  
Vol 6 (1) ◽  
Author(s):  
Aditya Agnihotri
Keyword(s):  
Hypergeometric Series ◽  
Basic Hypergeometric Series ◽  
Summation Formulae ◽  
Bilateral Basic Hypergeometric Series

In the present work, certain transformations and summation formulae for basic bilateral hypergeometric series have been discussed. This study also gives the method of obtaining new transformations and summation formulae for basic bilateral hypergeometric series. Some of the applications have been mentioned.

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