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.

Certain Summation Formulae for Basic Hypergeometric Series

1977 ◽  
Vol 20 (3) ◽  
pp. 369-375 ◽  
Author(s):  
Arun Verma
Keyword(s):  
Hypergeometric Series ◽  
Basic Hypergeometric Series ◽  
Summation Formulae ◽  
Image Position

In 1927, Jackson [5] obtained a transformation connecting awhere N is any integer, with aviz.,1where | q | > l and |qγ-α-βN| > l.

scholarly journals TRANSFORMATION AND REDUCTION FORMULAE FOR DOUBLE q-SERIES OF TYPE Φ2:1;λ2:0;μ

2009 ◽  
Vol 52 (1) ◽  
pp. 195-204 ◽  
Author(s):  
CANGZHI JIA ◽  
XIANGDE ZHANG
Keyword(s):  
Hypergeometric Series ◽  
Basic Hypergeometric Series ◽  
General Transformation ◽  
Summation Formulae

AbstractBy applying the Sears non-terminating transformations, we establish four general transformation theorems for double basic hypergeometric series of type Φ2:1;λ2:0;μ. Moreover, several transformation, reduction and summation formulae on the double basic hypergeometric series Φ2:1;22:0;1, Φ2:1;32:0;2 and Φ2:1;42:0;3 are also derived through parameter specialisation.

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.

scholarly journals Non-Terminating Basic Hypergeometric Series and the q-Zeilberger Algorithm

2008 ◽  
Vol 51 (3) ◽  
pp. 609-633 ◽  
Author(s):  
William Y. C. Chen ◽  
Qing-Hu Hou ◽  
Yan-Ping Mu
Keyword(s):  
Recurrence Relation ◽  
Hypergeometric Series ◽  
Basic Hypergeometric Series ◽  
Systematic Method ◽  
Limit Values ◽  
Summation Formulae ◽  
Classical Transformation ◽  
Almost All ◽  
Limiting Case ◽  
Summation Index

AbstractWe present a systematic method for proving non-terminating basic hypergeometric identities. Assume that k is the summation index. By setting a parameter x to xqn, we may find a recurrence relation of the summation by using the q-Zeilberger algorithm. This method applies to almost all non-terminating basic hypergeometric summation formulae in the work of Gasper and Rahman. Furthermore, by comparing the recursions and the limit values, we may verify many classical transformation formulae, including the Sears–Carlitz transformation, transformations of the very well-poised 8φ7 series, the Rogers–Fine identity and the limiting case of Watson's formula that implies the Rogers–Ramanujan identities.

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.

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