Results 31 to 40 of about 5,265 (203)
Fractal and Fractional, 2023 In the geometric function theory of complex analysis, the investigation of the geometric properties of analytic functions using q-analogues of differential and integral operators is an important area of study, offering powerful tools for applications in ...
Suha B. Al-Shaikh +3 more
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q-Calculus as operational algebra; pp. 73–97 [PDF]
Proceedings of the Estonian Academy of Sciences, 2009 This second paper on operational calculus is a continuation of Ernst, T. q-Analogues of some operational formulas. Algebras Groups Geom., 2006, 23(4), 354â374. We find multiple q-analogues of formulas in Carlitz, L.
Thomas Ernst
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Some Remarks on Very-Well-Poised 8ϕ7 Series
Symmetry, Integrability and Geometry: Methods and Applications, 2012 Nonpolynomial basic hypergeometric eigenfunctions of the Askey-Wilson second order difference operator are known to be expressible as very-well-poised 8ϕ7 series.
Jasper V. Stokman
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On generalization of continued fraction of Gauss
International Journal of Mathematics and Mathematical Sciences, 1990 In this paper we establish a continued fraction represetation for the ratio qf two basic bilateral hypergeometric series 2ψ2's which generalize Gauss' continued fraction for the ratio of two 2F1's.
Remy Y. Denis
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On a New Summation Formula for 𝟐𝜓𝟐 Basic Bilateral Hypergeometric Series and Its Applications
International Journal of Mathematics and Mathematical Sciences, 2011 We have obtained a new summation formula for 2𝜓2 bilateral basic hypergeometric series by the method of parameter augmentation and demonstrated its various uses leading to some development of etafunctions, 𝑞-gamma, and 𝑞-beta function identities.
D. D. Somashekara +2 more
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Mathematics, 2020 This contribution deals with the sequence {Un(a)(x;q,j)}n≥0 of monic polynomials in x, orthogonal with respect to a Sobolev-type inner product related to the Al-Salam–Carlitz I orthogonal polynomials, and involving an arbitrary number j of q-derivatives ...
Carlos Hermoso +3 more
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Parameter Augmentation for Basic Hypergeometric Series, I
Journal of Combinatorial Theory, Series A, 1997 [For part I see the authors in Prog. Math. 161, 111--129 (1998; Zbl 0901.33008).] Let \(D_q\) be the \(q\)-difference operator, \( D_qf(a) = (f(a) - f(aq))/a\), and define an exponential operator \(T\) by \[ T(bD_q) = \sum_{n=0}^{\infty} {(bD_q)^n \over (q;q)_n}. \] The authors derive many known results by applying this operator to simpler results.
Chen, William Y.C, Liu, Zhi-Guo
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A multipoint conformal block chain in d dimensions
Journal of High Energy Physics, 2020 Conformal blocks play a central role in CFTs as the basic, theory-independent building blocks. However, only limited results are available concerning multipoint blocks associated with the global conformal group.
Sarthak Parikh
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Microglial GPR35 Ameliorates Epileptogenesis and Neuroinflammation via PDGFA Domain 2 Signaling
Advanced Science, EarlyView.Activation of microglial G protein–coupled receptor 35 (GPR35) by L‐kynurenic acid (L‐Kyna) initiates a platelet‐derived growth factor A (PDGFA)–dependent phosphoinositide 3‐kinase–protein kinase B (PI3K–AKT) signaling cascade that dampens hippocampal neuroinflammation, thereby restraining epileptogenesis, lowering seizure susceptibility, and ...
Qi Wang +17 more
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Generating functions for some families of the generalized Al-Salam–Carlitz q-polynomials
Advances in Difference Equations, 2020 In this paper, by making use of the familiar q-difference operators D q $D_{q}$ and D q − 1 $D_{q^{-1}}$ , we first introduce two homogeneous q-difference operators T ( a , b , c D q ) $\mathbb{T}(\mathbf{a},\mathbf{b},cD_{q})$ and E ( a , b , c D q − 1 )
Hari Mohan Srivastava, Sama Arjika
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