Results 31 to 40 of about 6,972,539 (190)
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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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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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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Approach of $q$-Derivative Operators to Terminating $q$-Series Formulae [PDF]
, 2018 summary:The $q$-derivative operator approach is illustrated by reviewing several typical summation formulae of terminating basic hypergeometric ...
Wang, Xiaoyuan, Chu, Wenchang
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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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RESULTS ON BASIC HYPERGEOMETRIC SERIES AND CONTINUED FRACTIONS
JOURNAL OF RAMANUJAN SOCIETY OF MATHEMATICS AND MATHEMATICAL SCIENCES, 2022 In this paper, making use of certain known identities, we have established some result involving q-series and continued fractions.
Pant, G. S., Chand, K. B.
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Nonsymmetric interpolation Macdonald polynomials and g_n basic hypergeometric series
, 2009 30 pagesInternational audienceThe Knop-Sahi interpolation Macdonald polynomials are inhomogeneous and nonsymmetric generalisations of the well-known Macdonald polynomials. In this paper we apply the interpolation Macdonald polynomials to study a new type
Lascoux, Alain +2 more
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MagmaFlow: A desktop platform for artificial intelligence‐driven expression analysis
FEBS Open Bio, EarlyView.MagmaFlow is a free, no‐code platform for gene expression analysis. It generates interactive volcano plots, links genes to literature, pathways, and diseases, prioritizes candidates using millions of publications, identifies affected biological processes, builds network diagrams, and exports publication‐ready figures and reports for macOS and Windows ...
Carlos E. Buss +7 more
wiley +1 more source
A τ-Deformation of the Basic Horn Function H3 in q-Calculus
Journal of Function SpacesMotivated by the growing literature on basic (or q-) Horn-type series in quantum calculus and by τ-extensions of hypergeometric functions, we introduce a generalized basic τ-confluent Horn hypergeometric function H3.
Maryam G. Alshehri +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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