Results 31 to 40 of about 5,104 (194)
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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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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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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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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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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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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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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Molecular Oncology, EarlyView.Generation of two normal and tumour (cancerous) paired human cell lines using an established tissue culture technique and their characterisation is described. Cell lines were characterised at cellular, protein, chromosome and gene expression levels and for HPV status.
Simon Broad +12 more
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Advanced Science, EarlyView.YAP undergoes phase separation to activate the AJUBA super‐enhancer, driving aberrant mitosis through spindle checkpoint dysregulation in breast cancer. This study uncovers a mechanistic link between YAP condensates, super‐enhancer activation, and aneuploidy formation.
Rui Zhang +8 more
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