\(q\)-Gevrey asymptotic expansion and Jacobi theta function.

DOI10.1016/S1631-073X(02)02586-4zbMath1025.39014MaRDI QIDQ1565893

Changgui Zhang, Jean Pierre Ramis

Publication date: 27 May 2003

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

zbMATH Keywords

elliptic functions\(q\)-difference equationsJacobi theta function\(q\)-Gevrey asymptotic expansion

Mathematics Subject Classification ID

Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Entire functions of one complex variable (general theory) (30D20) Difference equations, scaling ((q)-differences) (39A13) Elliptic functions and integrals (33E05)

Related Items (14)

On the summability of a class of formal power series ⋮ Isomonodromic deformation of 𝑞-difference equations and confluence ⋮ q-Analogues of Laplace and Borel transforms by means of q-exponentials ⋮ Solutions of linear systems of moment differential equations via generalized matrix exponentials ⋮ On \(q\)-asymptotics for linear \(q\)-difference-differential equations with Fuchsian and irregular singularities ⋮ Meromorphic solutions of linear \(q\)-difference equations ⋮ q-Borel-Laplace summation for q–difference equations with two slopes ⋮ \(q\)-deformation of meromorphic solutions of linear differential equations ⋮ On functional linear partial differential equations in Gevrey spaces of holomorphic functions ⋮ On parametric multilevel \(q\)-Gevrey asymptotics for some linear \(q\)-difference-differential equations ⋮ On singularly perturbed \(q\)-difference-differential equations with irregular singularity ⋮ On \(q\)-summation and confluence ⋮ Confluence of meromorphic solutions of \(q\)-difference equations ⋮ On the archimedean and nonarchimedean 𝑞-Gevrey orders

Cites Work

• Unnamed Item
• 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.)
• Summability of divergent series
• Transformations de q-Borel–Laplace au moyen de la fonction thêta de Jacobi

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