Results 21 to 30 of about 584 (125)
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.
Saloni Kushvaha, S. Ahmad Ali
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Asymptotic formulae of two divergent bilateral basic hypergeometric series
, 2016 We provide new formulae for the degenerations of the bilateral basic hypergeometric function ${}_1 _1 ( a; b; q, z )$ with using the $q$-Borel-Laplace transformation. These are thought of as the first step to construct connection formulae of $q$-difference equation for ${}_1 _1 ( a; b; q, z )$.
Mori, Hironori, Morita, Takeshi
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Transformations and summations for bilateral basic hypergeometric series
We derive transformation and summation formulas for bilateral basic hypergeometric series. As a starting point, we use two transformations of bilateral basic very-well-poised ${}_8Ψ_8$. The first transformation is given as a sum of two nonterminating ${}_8W_7$'s and the second is given in terms of a sum of a ${}_4ψ_4$ and two balanced ${}_4ϕ_3$'s. From
Cohl, Howard S., Schlosser, Michael J.
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On transformation of certain bilateral basic hypergeometric series and their applications
Proceedings - Mathematical Sciences, 2019 In this paper, the authors presented transformation and summation formulae for bilateral basic hypergeometric series: \[\sum_{n=-\infty}^{\infty}\frac{(a)_n}{(b)_n}z^n= \frac{(b/a;q)_\infty}{(b,bz/a;q)_\infty}\sum_{n=-\infty}^{\infty}(a)_nz^n\] whenever \(\max\{|b/a|,|1/b|\}
Somashekara, D. D., Vidya, K. N.
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Mock Theta Function Identities Deriving from Bilateral Basic Hypergeometric Series [PDF]
, 2017 The bilateral series corresponding to many of the third-, fifth-, sixth- and eighth order mock theta functions may be derived as special cases of $_2 _2$ series \[ \sum_{n=-\infty}^{\infty}\frac{(a,c;q)_n}{(b,d;q)_n}z^n. \] Three transformation formulae for this series due to Bailey are used to derive various transformation and summation formulae for ...
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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.
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Summation formulae for the bilateral basic hypergeometric series ${}_1��_1 ( a; b; q, z )$
, 2016 17 ...
Mori, Hironori, Morita, Takeshi
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On a ${\mathbb C}^2$-valued integral index transform and bilateral hypergeometric series
, 2021 We discuss the spectral decomposition of the hypergeometric differential operators on the line $\mathrm{Re}\, z=1/2$. Such operators arise in the problem of decomposition of tensor products of unitary representations of the universal covering of the group $SL(2\,{\mathbb R}$.
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An asymptotic formula of the divergent bilateral basic hypergeometric series
, 2012 We show an asymptotic formula of the divergent bilateral basic hypergeometric series ${}_1 _0 (a;-;q,\cdot)$ with using the $q$-Borel-Laplace method. We also give the limit $q\to 1-0$ of our asymptotic formula.
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