About Jackson \(q\)-Bessel functions

DOI10.1016/S0021-9045(03)00073-XzbMath1023.33012MaRDI QIDQ1395805

Changgui Zhang

Publication date: 1 July 2003

Published in: Journal of Approximation Theory (Search for Journal in Brave)

zbMATH Keywords

connection matrixJacobi's theta function\(q\)-Bessel function\(q\)-Borel-Laplace transform

Mathematics Subject Classification ID

Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15)

Related Items (10)

On symmetric solutions of the fourth q-Painlevé equation ⋮ A modular-type formula for \((x;q)_\infty \) ⋮ Zeros of entire functions and a problem of Ramanujan ⋮ Analytical study of the pantograph equation using Jacobi theta functions ⋮ On \(q\)-advanced spherical Bessel functions of the first kind and perturbations of the Haar wavelet ⋮ q-Borel-Laplace summation for q–difference equations with two slopes ⋮ The Stokes phenomenon for the \(q\)-difference equation satisfied by the Ramanujan entire function ⋮ \(q\)-deformation of meromorphic solutions of linear differential equations ⋮ On \(q\)-summation and confluence ⋮ Confluence of meromorphic solutions of \(q\)-difference equations

Cites Work

• The zeros of basic Bessel functions, the functions J(nu+ax)(x), and associated orthogonal polynomials
• Développements asymptotiques \(q\)-Gevrey et séries \(Gq\)-sommables. (\(q\)-Gevrey asymptotic expansions and \(Gq\)-summable series.)
• Asymptotics of basic Bessel functions and \(q\)-Laguerre polynomials
• Galois theory of difference equations
• Theq-Gamma andq-Beta Functions†
• Linear 𝑞-difference equations
• Transformations de q-Borel–Laplace au moyen de la fonction thêta de Jacobi
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