On a New Summation Formula for πππ Basic Bilateral Hypergeometric Series and Its Applications [PDF]
International Journal of Mathematics and Mathematical Sciences, 2011 We have obtained a new summation formula for 2π2 bilateral basic hypergeometric series by the method of parameter augmentation and demonstrated its various uses leading to some development of etafunctions, π-gamma, and π-beta function identities.
D. D. Somashekara +2 more
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Summation formulae for the bilateral basic hypergeometric series ${}_1Ο_1 ( a; b; q, z )$ [PDF]
, 2016 17 ...
Hironori Mori, Takeshi Morita
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An asymptotic formula of the divergent bilateral basic hypergeometric series [PDF]
, 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.
Takeshi Morita
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Asymptotic formulae of two divergent bilateral basic hypergeometric series [PDF]
, 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 ${}_1 _1 ( a; b; q, z )$.
Hironori Mori, Takeshi Morita
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On a β2-valued integral index transform and bilateral hypergeometric series [PDF]
Integral Transforms and Special Functions, 2022 We discuss the spectral decomposition of the hypergeometric differential operators on the line Rez=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,R). Our main purpose is a search of natural bases in generalized eigenspaces and variants of the inversion ...
Yury A. Neretin
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On certain relations between products of bilateral hypergeometric series [PDF]
Proceedings of the Glasgow Mathematical Association, 1957 Darling [3] in 1932 and Bailey [2] in 1933 gave certain theorems on products of hypergeometric series. Again in 1948 Sears [4] used the relation which expresses the series in terms of M other series of the same type to derive transformations between products of both basic and ordinary hypergeometric series. In this paper I give certain general theorems
Harishanker Shukla
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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 ...
James Mc Laughlin
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Transformations and summations for bilateral basic hypergeometric series [PDF]
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 ${}_8Ξ¨_8$. 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 ${}_4Ο_4$ and two balanced ${}_4Ο_3$'s. From
Howard S. Cohl, Michael J. Schlosser
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Some more semi-finite forms of bilateral basic hypergeometric series [PDF]
, 2005 9 ...
FrΓ©dΓ©ric Jouhet
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On a ${\mathbb C}^2$-valued integral index transform and bilateral hypergeometric series [PDF]
, 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 $SL(2\,{\mathbb R}$.
Yury A. Neretin
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