On \(q\)-summation and confluence
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Publication:1010977
DOI10.5802/aif.2433zbMath1175.34111arXiv0709.1610OpenAlexW1639320165MaRDI QIDQ1010977
Lucia Di Vizio, Changgui Zhang
Publication date: 7 April 2009
Published in: Annales de l'Institut Fourier (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0709.1610
Difference equations, scaling ((q)-differences) (39A13) (q)-gamma functions, (q)-beta functions and integrals (33D05) Stokes phenomena and connection problems (linear and nonlinear) for ordinary differential equations in the complex domain (34M40)
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Cites Work
- On \(q\)- difference functional equations
- About the growth of entire functions solutions of linear algebraic \(q\)- difference equations
- Développements asymptotiques \(q\)-Gevrey et séries \(Gq\)-sommables. (\(q\)-Gevrey asymptotic expansions and \(Gq\)-summable series.)
- About Jackson \(q\)-Bessel functions
- Arithmetic theory of \(q\)-difference equations. The \(q\)-analogue of Grothendieck-Katz's conjecture on \(p\)-curvatures
- \(q\)-Gevrey asymptotic expansion and Jacobi theta function.
- Systèmes aux \(q\)-différences singuliers réguliers : classification, matrice de connexion et monodromie. (Regular singular \(q\)-difference systems: Classification, connection matrix and monodromy)
- Gevrey series of arithmetic type. I: Purity and duality theorems
- Multisummability of formal power series solutions of linear analytic \(q\)-difference equations.
- The canonical slope filtration of a \(q\)-difference module
- The canonical filtration by the slopes of a \(q\)-difference module and the associated graded module.
- Formal solutions of linear meromorphic differential systems and summability
- Summability of divergent series
- On integral representations of \(q\)-gamma and \(q\)-beta functions
- Transformations de q-Borel–Laplace au moyen de la fonction thêta de Jacobi
- On Jackson's \(q\)-gamma function
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