General Transformations of Bilateral Cognate Trigonometrical Series of Ordinary Hypergeometric Type [PDF]
Canadian Journal of Mathematics, 1953 Whipple [6] was the first to consider transformations connecting well-poised hypergeometric series as particular cases of relations between cognate trigonometrical series. He used contour integrals of the Barnes type to deduce such transformations. Later Sears [3] gave a systematic
Ravi P. Agarwal
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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.
Pankaj Srivastava
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ON BILATERAL BASIC HYPERGEOMETRIC SERIES AND CONTINUED FRACTIONS
International Journal of Apllied Mathematics, 2013 Summary: This article deals with the derivation of continued fraction involving bilateral basic hypergeometric series by making use of known three term relations and other known results of R. P. Agarwal.
Pankaj Srivastava, Debasisha Mishra
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Certain Transformations of Nearly-Poised Bilateral Hypergeometric Series of Special Type [PDF]
Canadian Journal of Mathematics, 1958 A few years ago Bailey (1) gave certain transformations of both terminating and non-terminating nearly-poised hypergeometric series of the ordinary type and later on he also deduced basic analogues of some of his transformations. Recently, (3) I gave certain transformations of both ordinary and basic terminating nearly-poised bilateral hypergeometric ...
H. S. Shukla
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CERTAIN NEW IDENTITIES OF BASIC BILATERAL HYPERGEOMETRIC SERIES
South East Asian J. of Mathematics and Mathematical SciencesIn 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.
Shoukat Ali, Saloni Kushvaha
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On Certain Transformations of Poly-Basic Bilateral Hypergeometric Series [PDF]
International Journal of Science and Research (IJSR), 2021 Brijesh Singh
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On certain transformations of poly-basic bilateral hypergeometric series
Journal of Computational and Applied Mathematics, 2003 The authors establish transformations of poly-basic bilateral hypergeometric series in terms of another similar series not necessary having the same number of bases. As application of the obtained results, they derive expressions of the product of two \(q\)-series in terms of another product of two series which lead to interesting transformations of ...
R. Y. Denis, S. N. Singh, Satya P. Singh
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A NOTE ON TRANSFORMATION FORMULAE FOR BILATERAL BASIC HYPERGEOMETRIC SERIES [PDF]
International Journal of Apllied Mathematics, 2013 Pankaj Srivastava +3 more
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Bilateral inversions and terminating basic hypergeometric series identities
Discrete Mathematics, 2008 A \(q\)-analogue of the Legendre inversion is established and generalized to bilateral sequences. They are employed to investigate the dual relations of three basic formulae due to Jackson and Bailey, on balanced \(_{3}\phi_{2}\)-series, well-poised \(_{8}\phi_{7}\)-series and bilateral \(_{6}\psi_{6}\)-series.
Wenchang Chu, Chenying Wang
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On the Very-well-poised Bilateral Basic Hypergeometric $_5ψ_5$ Series [PDF]
, 2016 This paper has been withdrawn by the author due to some errors in the ...
Runping Ye, Qing Zou
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