The $q$-Laplace Transforms compared: the basic confluent hypergeometric function ${}_2\ddot{I}{•}_0$

Daniel Meikle, Adri Olde Daalhuis

In solving $q$-difference equations, and in the definition of $q$-special functions, we encounter formal power series in which the $n$th coefficient is of size $q^{-\left(\genfrac{}{}{0ex}{}{n}{2}\right)}$…