Results 21 to 30 of about 5,152 (170)
Bijective proofs of basic hypergeometric series identities [PDF]
Pacific Journal of Mathematics, 1987 The authors give simple, completely bijective proofs of the \(q\)-binomial theorem and Heine's \({}_2\Phi_1\) transformation. Since all identities on basic hypergeometric series can be built out of these two fundamental identities, any basic hypergeometric identity can be proved bijectively, at least in theory, by building bijections out of these ...
Joichi, J. T., Stanton, Dennis
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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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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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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.
William Y. C. Chen, Zhi-Guo Liu
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Lattice paths and multiple basic hypergeometric series [PDF]
Pacific Journal of Mathematics, 1989 The equivalence between certain identities for basic hypergeometric series and some combinatorial identities for colored partitions is established by viewing the basic hypergeometric series as generating functions for weighted lattice paths.
Agarwal, A. K., Bressoud, David M.
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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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Advanced Science, EarlyView.A multifunctional nanoagonist (cDZ@IP) enables nano‐metabolite–driven multimodal activation of the STING pathway and enhanced immune recognition, achieving potent antitumor immunity and suppressing tumor growth and metastasis. This strategy highlights the rational design of therapeutic metabolites and establishes a new paradigm bridging nanomedicine ...
Kepeng Hu +17 more
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