Results 81 to 90 of about 6,972,539 (190)
EncyclopediaThe observation of randomness patterns serves as guidance for the craft of probabilistic modelling. The most used count models—Binomial, Poisson, Negative Binomial—are the discrete Morris’ natural exponential families whose variance is at most quadratic ...
Sandra Mendonça +3 more
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History, development and application of basic Hypergeometric Series
The basic hypergeometric series, a powerful tool in the field of mathematical analysis, traces its origins to the study of special functions and q-series. Introduced by mathematicians in the early 20th century, it has since evolved to play a crucial role
Gagendra Bhandari
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Two Inequalities for
Journal of Inequalities and Applications, 2008 We use the -binomial formula to establish two inequalities for the basic hypergeometric series . As applications of the inequalities, we discuss the convergence of -series.
Wang Mingjin
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CAUCHY\u27S METHOD AND BILATERAL BASIC HYPERGEOMETRIC SERIES
, 2013 In this paper, we find bilateral basic hypergeometric series adapting Cauchy’s method used by Bailey, Slater, Fredric Jouhet and Michael ...
Antony, Roselin, Fiseha, Hailemariam
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On Convergence of
Journal of Inequalities and Applications, 2009 We use inequality technique and the terminating case of the -binomial formula to give some results on convergence of -series involving basic hypergeometric series.
Zhao Xilai, Wang Mingjin
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The q-Borel Sum of Divergent Basic Hypergeometric Series ᵣφₛ(a; b; q, x)
, 2019 We study the divergent basic hypergeometric series, which is a q-analog of divergent hypergeometric series. This series formally satisfies the linear q-difference equation.
Adachi, S.
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A note on certain classes of multivariable q-series transformations
Le Matematiche, 2010 The present note envisage to derive some new classes of multiple q-series transformations and reduction formulae. Special cases in terms ofthe known and new results are also derived.
Sunil Dutt Purohit, Rajendra Kumar Yadav
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Two types of series expansions valid at strong coupling
Journal of High Energy PhysicsIt is known that perturbative expansions in powers of the coupling in quantum mechanics (QM) and quantum field theory (QFT) are asymptotic series. This can be useful at weak coupling but fails at strong coupling.
Ariel Edery
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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.
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Certain Transformations of Nearly-Poised Bilateral Hypergeometric Series of Special Type
, 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 ...
H. S. Shukla
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