On some $q$-versions of Ramanujan master theorem
In this paper, we state some $q$-analogues of the famous Ramanujan's Master Theorem. As applications, some values of Jackson's $q$-integrals involving $q$-special functions are computed.
math.CA↗
arXiv subjects
Neji Bettaibi
Publications and source records attributed to Neji Bettaibi.
Wavelet Transforms Associated With the Basic Bessel Operator
This paper aims to study the $q$-wavelet and the $q$-wavelet transforms, associated with the $q$-Bessel operator for a fixed $q\in ]0, 1[$. As an application, an inversion formulas of the $q$-Riemann-Liouville and $q$-Weyl transforms using $q$-wavelets are given. For this purpose, we shall attempt to extend the classical theory by giving their $q$-analogues.
math.QA↗
Uncertainty Principles for the Fourier Transforms in Quantum Calculus
Some properties of the $q$-Fourier-sine transform are studied and $q$-analogues of the Heisenberg uncertainty principle is derived for the $q$-Fourier-cosine transform studied in \cite{FB} and for the $q$-Fourier-sine transform.
math.QA↗