Results 11 to 20 of about 66 (51)

On certain transformations of nearly-poised basic bilateral hypergeometric series of the type M ? M

Mathematische Zeitschrift, 1958
exaly   +2 more sources

A Bilateral Series Involving Basic Hypergeometric Functions [PDF]

, 2005
We prove a summation formula for a bilateral series whose terms are products of two basic hypergeometric functions. In special cases, series of this type arise as matrix elements of quantum group representations.
openaire   +2 more sources

New Mock Theta Function Identities via Fractional q-Calculus and Bilateral ₂ψ₂ Series

Fractal and Fractional
Mock theta functions, introduced by Ramanujan in his last letter to Hardy, play a significant role in q-series theory and have natural connections to fractional q-calculus. In this paper, we study bilateral hypergeometric series of the form ψ22= ∑n=−∞∞(a,
Qiuxia Hu, Bilal Khan
doaj   +1 more source

Transformations and Summations for Bilateral Basic Hypergeometric Series

Arabian Journal of Mathematics
Abstract We review and derive transformation and summation formulas for bilateral basic hypergeometric series. Our study focuses on consequences of certain bilateral extensions of two important results by Bailey, namely a transformation for very-well-poised
Howard S. Cohl, Michael J. Schlosser
openaire   +2 more sources

Bilateral Basic Hypergeometric Series: A Study

Anusandhaan - Vigyaan Shodh Patrika, 2018
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.
openaire   +1 more source

On the very-well-poised bilateral basic hypergeometric ψ77 series

Journal of Mathematical Analysis and Applications, 2010
AbstractThe purpose of this paper is to derive several new transformation formulas between bilateral and unilateral basic hypergeometric series by making use of a method which was first used by Watson and later more systematically employed by Bailey.
Zhang, Zhizheng, Hu, Qiuxia
  +4 more sources

On the Very-well-poised Bilateral Basic Hypergeometric $_5ψ_5$ Series

, 2016
This paper has been withdrawn by the author due to some errors in the ...
Ye, Runping, Zou, Qing
openaire   +2 more sources

CERTAIN NEW IDENTITIES OF BASIC BILATERAL HYPERGEOMETRIC SERIES

South East Asian J. of Mathematics and Mathematical Sciences
In the present work, we have applied Cauchy’s method to establish some basic bilateral hypergeometric series identities, using the known identities of terminating unilateral series. We also have discussed some important special cases of our results.
Saloni Kushvaha, S. Ahmad Ali
openaire   +1 more source

Resonance of Continued Fractions Related to₂ψ₂Basic Bilateral Hypergeometric Series [PDF]

Kyungpook mathematical journal, 2011
Summary: In this paper, making use of transformation due to \textit{S. N. Singh} [Proc. Natl. Acad. Sci. India, Sect. A 65, No.3, 319--329 (1995; Zbl 0992.33501)], an attempt has been made to establish certain results involving basic bilateral hypergeometric series and continued fractions.
openaire   +2 more sources

Several transformation formulas involving bilateral basic hypergeometric series

, 2019
In terms of the analytic continuation method, we prove three transformation formulas involving bilateral basic hypergeometric series. One of them is equivalent to Jouhet's result involving two $_8ψ_8$ series and two $_8ϕ_7$ series.
Wei, Chuanan, Yu, Tong
openaire   +2 more sources