Results 21 to 30 of about 66 (51)
Asymptotic formulae of two divergent bilateral basic hypergeometric series
, 2016 We provide new formulae for the degenerations of the bilateral basic hypergeometric function ${}_1ψ_1 ( a; b; q, z )$ with using the $q$-Borel-Laplace transformation. These are thought of as the first step to construct connection formulae of $q$-difference equation for ${}_1ψ_1 ( a; b; q, z )$. Moreover, we show that our formulae have the $q \to 1 - 0$
Mori, Hironori, Morita, Takeshi
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Summation formulae for the bilateral basic hypergeometric series ${}_1ψ_1 ( a; b; q, z )$
, 2016 We give summation formulae for the bilateral basic hypergeometric series ${}_1ψ_1( a; b; q, z )$ through Ramanujan's summation formula, which are generalizations of nontrivial identities found in the physics of three-dimensional Abelian mirror symmetry on $\mathbf{R}P^2 \times S^1$. We also show the $q \to 1 - 0$ limit of our summation formulae.
Mori, Hironori, Morita, Takeshi
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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 $_2ψ_2$ 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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An asymptotic formula of the divergent bilateral basic hypergeometric series
, 2012 We show an asymptotic formula of the divergent bilateral basic hypergeometric series ${}_1ψ_0 (a;-;q,\cdot)$ with using the $q$-Borel-Laplace method. We also give the limit $q\to 1-0$ of our asymptotic formula.
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A NOTE ON TRANSFORMATION FORMULAE FOR BILATERAL BASIC HYPERGEOMETRIC SERIES [PDF]
International Journal of Apllied Mathematics, 2013 Srivastava, Pankaj +3 more
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Theta functions and transformations of bilateral basic hypergeometric series
We establish new transformation formulas involving theta functions and certain bilateral basic hypergeometric series. From these formulas, we construct companion $q$-series for a class of $q$-series such that the asymptotic expansion of their quotient admits a simple closed form.
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On Certain Transformations of Poly-Basic Bilateral Hypergeometric Series
International Journal of Science and Research (IJSR), 2021 openaire +1 more source
We use a new $q$-exponential operator based on the $q^{\pm1}$-derivative $\D_{q^{\pm1}}$ of order 1 to derive summation formulas for bilateral basic hypergeometric series ${}_{0}ψ_{1}$, ${}_{1}ψ_{1}$, ${}_{1}ψ_{2}$, and ${}_{2}ψ_{2}$. In addition, we provide summation formulas for bilateral series whose terms are basic hypergeometric functions.
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The Saalschütz chain reactions and bilateral basic hypergeometric series
Constructive Approximation, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wenchang Chu, Chu Wenchang
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