Results 161 to 170 of about 5,521 (197)

Summations for basic hypergeometric series involving a q-analogue of the digamma function

Computers and Mathematics With Applications, 1996
Using a simple method, numerous summation formulas for hypergeometric and basic hypergeometric series are derived. Among these summation formulas are nonterminating extensions and q-extensions of identities recorded by Lavoie, Luke, Watson, and ...
C Krattenthaler, H M Srivastava
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Two new transformation formulas of basic hypergeometric series

Journal of Mathematical Analysis and Applications, 2007
By means of a modified version of Cauchy's method for obtaining bilateral series identities, two new transformation formulas for bilateral basic hypergeometric series are derived. These contain several important identities for basic hypergeometric series
Zhizheng Zhang
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Summation theorems for multidimensional basic hypergeometric series by determinant evaluations

Discrete Mathematics, 2000
We derive summation formulas for a specific kind of multidimensional basic hypergeometric series associated to root systems of classical type. We proceed by combining the classical (one-dimensional) summation formulas with certain determinant evaluations.
Michael J Schlosser
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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.
Medhat Ahmed Rakha, Essam S. El-Sedy
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Reduction and transformation formulae for bivariate basic hypergeometric series

Journal of Mathematical Analysis and Applications, 2007
The main object of this paper is to establish several bivariate basic hypergeometric series identities by means of elementary series manipulation.
Jia, C.-Z., Wang, T.-M.
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On certain transformations of poly-basic bilateral hypergeometric series

Journal of Computational and Applied Mathematics, 2003
In this paper, we have established certain transformations of basic hypergeometric series with more than one base. Some of these lead to the relationship between product of two q-series. These results, in turn, lead to very interesting transformations of
Singh, S.N., Denis, Remy Y., Singh, S.P.
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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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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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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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Some identities between basic hypergeometric series deriving from a new Bailey-type transformation

Journal of Mathematical Analysis and Applications, 2008
We prove a new Bailey-type transformation relating WP-Bailey pairs. We then use this transformation to derive a number of new 3- and 4-term transformation formulae between basic hypergeometric ...
James Mc Laughlin
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