The \(q\)-Borel sum of divergent basic hypergeometric series \(_r\phi_s(a;b;q,x)\)

DOI10.3842/SIGMA.2019.016zbMath1428.33031arXiv1806.05375OpenAlexW2807751654MaRDI QIDQ2633032

Shunya Adachi

Publication date: 8 May 2019

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.05375

zbMATH Keywords

\(q\)-difference equationbasic hypergeometric seriesdivergent power series solution\(q\)-Borel summability\(q\)-Stokes

Mathematics Subject Classification ID

Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Difference equations, scaling ((q)-differences) (39A13) Asymptotics and summation methods for ordinary differential equations in the complex domain (34M30)

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Exact WKB analysis of \(\mathbb{C} \mathbb{P}^1\) holomorphic blocks

Cites Work

• Confluence of meromorphic solutions of \(q\)-difference equations
• On \(q\)-summation and confluence
• About the growth of entire functions solutions of linear algebraic \(q\)- difference equations
• Systèmes aux \(q\)-différences singuliers réguliers : classification, matrice de connexion et monodromie. (Regular singular \(q\)-difference systems: Classification, connection matrix and monodromy)
• q-Borel-Laplace summation for q–difference equations with two slopes
• Remarks on Some Basic Hypergeometric Series
• Building Meromorphic Solutions ofq-Difference Equations Using a Borel–Laplace Summation
• Theq-Gamma andq-Beta Functions†
• The Stokes phenomenon for the $q$-difference equation satisfied by the basic hypergeometric series ${}_3\varphi_1(a_1,a_2,a_3;b_1;q,x)$
• GENERAL TRANSFORMATIONS OF BILATERAL SERIES
• The Borel sum of divergent Barnes hypergeometric series and its application to a partial differential equation
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