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A Generalised Hypergeometric Function [PDF]
Proceedings of the Edinburgh Mathematical Society, 1956 The hypergeometric function1F(a, b; c; z) is analytic in the domain |arg(−z)| < π, and, when |z| < 1, may be represented by the seriesWhen |z| = 1 in the domain |arg(−z)| <π, this series converges2 to F(a; b; c; z) if R(a+b−c) < 0 (integral values of a, b and c are excluded in the present paper).
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Monodromy of A-hypergeometric functions [PDF]
Journal für die reine und angewandte Mathematik, 2014 Abstract Using Mellin–Barnes integrals we give a method to compute elements of the monodromy group of an A-hypergeometric system of differential equations. The method works under the assumption that the A-hypergeometric system has a basis of solutions consisting of Mellin–Barnes integrals.
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Open Physics, 2022 The main aim of this article is to study a new generalizations of the Gauss hypergeometric matrix and confluent hypergeometric matrix functions by using two-parameter Mittag–Leffler matrix function.
Jain Shilpi +4 more
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Advanced Science, EarlyView.ABSTRACT Accumulating evidence suggests that the intestinal microbiota participates in the progression of metabolic dysfunction‐associated steatotic liver disease (MASLD) through microbiota‐host interaction. However, the beneficial role of commensal mycobiota in MASLD progression remains poorly understood.
Shuping Qiao +11 more
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Hypergeometric Functions for Function Fields
Finite Fields and Their Applications, 1995 Let \(\{a,b,c\}\) be complex constants. Then the famous Gauss hypergeometric equation is given by \[ z(1 - z) {d^2y \over dz^2} + \bigl( c - (a + b + 1) z \bigr) {dy \over dz} - aby = 0. \] One defines the Pochhammer symbol \((a)_n\) by \((a)_0 : = 1\) and for \(n > 1\), \((a)_n : = a(a + 1) (a + 2) (a + 3) \cdots (a + n - 1)\).
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On transformations of A-hypergeometric functions
Funkcialaj Ekvacioj, 2017 We propose a systematic study of transformations of $A$-hypergeometric functions. Our approach is to apply changes of variables corresponding to automorphisms of toric rings, to Euler-type integral representations of $A$-hypergeometric functions. We show that all linear $A$-hypergeometric transformations arise from symmetries of the corresponding ...
Forsgård, Jens +2 more
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Machine Learning for Green Solvents: Assessment, Selection and Substitution
Advanced Science, EarlyView.Environmental regulations have intensified demand for green solvents, but discovery is limited by Solvent Selection Guides (SSGs) that quantify solvent sustainability. Training a machine learning model on GlaxoSmithKline SSG, a database of sustainability metrics for 10,189 solvents, GreenSolventDB is developed. Integrated with Hansen solubility metrics,
Rohan Datta +4 more
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Computing Hypergeometric Functions Rigorously [PDF]
ACM Transactions on Mathematical Software, 2019 We present an efficient implementation of hypergeometric functions in arbitrary-precision interval arithmetic. The functions 0 F 1 , 1 F 1 , 2 F 1 , and 2 F 0
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On Summations of Generalized Hypergeometric Functions with Integral Parameter Differences
MathematicsIn this paper, we present an extension of the Karlsson–Minton summation formula for a generalized hypergeometric function with integral parameter differences.
Kirill Bakhtin, Elena Prilepkina
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CD4+ Tregs Drive Post‐Ischemic Sprouting Angiogenesis via Endothelial YY1/MAML1 Reactivation
Advanced Science, EarlyView.ABSTRACT Microvascular complications of diabetes are chronic diseases of small vessels. We previously found that CD4+ regulatory T‐cells (Tregs) are markedly reduced in type 2 diabetes (T2D) after ischemic injury in both mice and humans, and that Treg deficiency in immunodeficient mice impairs vascular regeneration.
Hang Qu +10 more
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