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Review of Some Identities Involving Basic Hypergeometric Series

Ghanshyam Pant
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Application of basic hypergeometric series

Applied Mathematics and Computation, 2004
The study of the average search costs in a digital search tree built from \(n\) random data relies on the explicit expression of the polynomial \(H_{n}(u)\), of degree \(n\) in \(u\), which has as the coefficient of \(u^{k}\) the expected number of nodes on this level.
Rakha, Medhat A., El-Sedy, Essam S.
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Dn Basic Hypergeometric Series

The Ramanujan Journal, 1999
The purpose of this paper is the study of multiple series extensions of basic hypergeometric series related to the root system \(D_n\). The starting point in this paper is a small change in the notation of \(C_n\) and \(D_n\) series to bring them closer to \(A_n\) series.
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CAUCHY AUGMENTATION FOR BASIC HYPERGEOMETRIC SERIES

Bulletin of the London Mathematical Society, 2004
The authors introduce a method which they call ``Cauchy augmentation'', in order to derive certain summation and transformation formulas for basic hypergeometric series from specializations of them. This method is essentially an application to those series of an identity, due to Cauchy, which gives the expansion of a power of \(x\) in terms of the \(q\)
Chen, William Y. C., Fu, Amy M.
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Ramanujan and hypergeometric and basic hypergeometric series

Russian Mathematical Surveys, 1990
An incomplete survey of hypergeometric series is given, and some of Ramanujan's work on hypergeometric and basic hypergeometric series is put into the general framework as we understand it now.
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Summation Formulas for Basic Hypergeometric Series

SIAM Journal on Mathematical Analysis, 1981
Summation formulas for basic hypergeometric series are derived which are q-analogues of Minton’s [J. Math. Phys., 11 (1970), pp. 1375–1376] and Karlsson’s [J. Math. Phys., 12 (1971), pp. 270–271] summation formulas for generalized hypergeometric series, and some interesting limit cases are considered.
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ON CERTAIN IDENTITIES INVOLVING BASIC (q) HYPERGEOMETRIC SERIES

South East Asian J. of Mathematics and Mathematical Sciences, 2022
In this paper we establish certain identities by making use of Bailey’s 2Ψ2 transformation formula. Special cases of these identities have also been discussed.
Singh, Chandan Kumar, Singh, Satya Prakash, Yadav, Vijay   +2 more
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Almost poised basic hypergeometric series

Proceedings of the Indian Academy of Sciences - Section A, 1987
A basic hypergeometric series with numerator parameters \(a_ 1,a_ 2,...,a_ r\) and denominator \(b_ 2,...,b_ r\), is defined as almost poised if \(b_ i=a_ iq^{\delta_ i}/a_ i\), where \(\delta_ i=0,1\), or 2, for \(2\leq i\leq r\). The author here obtains three identities for almost poised series with \(r=3\) and \(r=5\) when \(a_ 1=q^{-2n}\).
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Certain transformations involving basic hypergeometric series

Complex Variables, Theory and Application: An International Journal, 1992
In this paper an attempt has made to establish a new transformation formula for the basic analogue of Kampe de Fedriet function.
TH. M. Rassias, S.N. Singh
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