The \textit{q-j}\(_\alpha\) Bessel function

DOI10.1006/jath.2001.3645zbMath1003.33007OpenAlexW2076026597MaRDI QIDQ1599258

Fethi Bouzeffour, Ahmed Fitouhi, M. Moncef Hamza

Publication date: 7 August 2002

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

Full work available at URL: https://doi.org/10.1006/jath.2001.3645

zbMATH Keywords

\(q\)-derivative\(q\)-integral\(q\)-analogue of the Bessel function

Mathematics Subject Classification ID

Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) (q)-gamma functions, (q)-beta functions and integrals (33D05)

Related Items (31)

Real Paley-Wiener theorems for the Koornwinder-Swarttouw \(q\)-Hankel transform ⋮ Unnamed Item ⋮ On Nash and Carlson's inequalities for symmetric \(q\)-integral transforms ⋮ Calderón s reproducing Formula For q-Bessel operator ⋮ On a \(q\)-Paley--Wiener theorem ⋮ Bessel-Wright transform in the setting of quantum calculus ⋮ \(q\)-fractional calculus for Rubin's \(q\)-difference operator ⋮ On Hardy's inequality for symmetric integral transforms and analogous ⋮ Basic Fourier series: convergence on and outside the \(q\)-linear grid ⋮ Uncertainty principles for the \(q\)-Bessel windowed transform and localization operators ⋮ \(q\)-Bessel positive definite and \(D _{q }\)-completely monotonic functions ⋮ Inequalities related to the third Jackson \(q\)-Bessel function of order zero ⋮ Analytical approximation formulas in quantum calculus ⋮ Expansions in terms of \(q\)-Laguerre heat polynomials ⋮ On the connection between heat and wave problems in quantum calculus and applications ⋮ Positivity of the generalized translation associated with the \(q\)-Hankel transform ⋮ On some inequalities of uncertainty principles type in quantum calculus ⋮ Elements of harmonic analysis related to the third basic zero order Bessel function ⋮ Connecting mirror symmetry in 3D and 2D via localization ⋮ Unnamed Item ⋮ An uncertainty principle for the basic Bessel transform ⋮ Calderón's reproducing formula and uncertainty principle for the continuous wavelet transform associated with the \(q\)-Bessel operator ⋮ Uncertainty principles for the q-bessel fourier transform ⋮ A characterization of weighted Besov spaces in quantum calculus ⋮ Dynamics of the basic Bessel operator and related convolution operators on spaces of entire functions ⋮ Paley-Wiener theorem for the \(q\)-Bessel transform and associated \(q\)-sampling formula ⋮ Positivity of the generalized translation associated with theq-Hankel transform and applications ⋮ Unnamed Item ⋮ Wavelet Transforms in Quantum Calculus ⋮ Distribution of positive type in Quantum Calculus ⋮ On the generalized Hilbert transform and weighted Hardy spaces in \(q\)-Dunkl harmonic analysis

Cites Work

• The \(q\)-cosine Fourier transform and the \(q\)-heat equation
• Transformation intégrale de Weyl et théorème de Paley-Wiener associes à un opérateur différentiel singulier sur \((0,\infty)\)
• Heat ``polynomials for a singular differential operator on (0,\(\infty)\)
• Elements of q-harmonic analysis
• The q-analogue of the Laguerre polynomials
• On the zeros of the Hahn-Exton \(q\)-Bessel function and associated \(q\)- Lommel polynomials
• Expansions in Terms of Heat Polynomials and Associated Functions
• The Finite Calculus Associated with Bessel Functions
• On q-Analogues of the Fourier and Hankel Transforms
• Shorter Notes: A Simple Proof of Ramanujan's 1 Ψ 1 Sum
• The Structure of the Algebra of Hankel Transforms and the Algebra of Hankel-Stieltjes Transforms
• Ted Chihara and his work on orthogonal polynomials
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