The \textit{q-j}\(_\alpha\) Bessel function (Q1599258)

The authors study a \(q\)-analogue of the Bessel function \(j_{\alpha}(x)\) given by \[ j_{\alpha}(x)=2^{\alpha}\Gamma(\alpha+1)x^{-\alpha}J_{\alpha}(x), \] where \(J_{\alpha}(x)\) denotes the classical Bessel function of the first kind (of order \(\alpha\)). Several properties of these \(q\)-Bessel functions are obtained such as a number of \(q\)-integral representations and a convolution property.