Results 11 to 20 of about 5,265 (203)
Semi-finite forms of bilateral basic hypergeometric series [PDF]
Proceedings of the American Mathematical Society, 2005 We show that several classical bilateral summation and transformation formulas have semi-finite forms. We obtain these semi-finite forms from unilateral summation and transformation formulas. Our method can be applied to derive Ramanujan’s 1 ψ 1
Chen, William Y. C., Fu, Amy M.
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HiST: Histological Images Reconstruct Tumor Spatial Transcriptomics via MultiScale Fusion Deep Learning. [PDF]
Adv Sci (Weinh)HiST, a multiscale deep learning framework, reconstructs spatially resolved gene expression profiles directly from histological images. It accurately identifies tumor regions, captures intratumoral heterogeneity, and predicts patient prognosis and immunotherapy response.
Li W +8 more
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Extension of the q-Pfaff-Saalschütz Theorem by Two Integer Parameters
Mathematics, 2022 We investigate a class of terminating 3ϕ2-series that comes from the balanced series perturbed by two extra integer parameters. By making use of the linearization method, a general summation formula is established that extends the well-known q-Pfaff ...
Nadia N. Li, Wenchang Chu
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A General Family of q-Hypergeometric Polynomials and Associated Generating Functions
Mathematics, 2021 Basic (or q-) series and basic (or q-) polynomials, especially the basic (or q-) hypergeometric functions and the basic (or q-) hypergeometric polynomials are studied extensively and widely due mainly to their potential for applications in many areas of ...
Hari Mohan Srivastava, Sama Arjika
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Multiple big q-Jacobi polynomials [PDF]
Bulletin of Mathematical Sciences, 2020 Here, we investigate type II multiple big q-Jacobi orthogonal polynomials. We provide their explicit formulae in terms of basic hypergeometric series, raising and lowering operators, Rodrigues formulae, third-order q-difference equation, and we obtain ...
Fethi Bouzeffour, Mubariz Garayev
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Insights into glandular trichome biology from analysis of organ-specific gene expression programmes in cannabis, hop and tomato. [PDF]
Plant JSignificance Statement This study of three glandular trichome‐producing species (cannabis, hop and tomato) defines tissue‐specific transcriptomic atlases for five organs (trichome, flower, leaf, stem and root), providing co‐expression and gene regulatory networks and identifying candidate regulators of specialised metabolism in trichomes of each ...
Tamiru-Oli M +10 more
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$n$-color overpartitions, lattice paths, and multiple basic hypergeometric series [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 We define two classes of multiple basic hypergeometric series $V_{k,t}(a,q)$ and $W_{k,t}(a,q)$ which generalize multiple series studied by Agarwal, Andrews, and Bressoud.
Olivier Mallet
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The Bateman Functions Revisited after 90 Years—A Survey of Old and New Results
Mathematics, 2021 The Bateman functions and the allied Havelock functions were introduced as solutions of some problems in hydrodynamics about ninety years ago, but after a period of one or two decades they were practically neglected. In handbooks, the Bateman function is
Alexander Apelblat +2 more
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