  The "twisted Mellin transform" is a slightly modified version of the usual
classical Mellin transform on $L^2(\mathbb R)$. In this short note we
investigate some of its basic properties. From the point of views of
combinatorics one of its most important interesting properties is that it
intertwines the differential operator, $df/dx$, with its finite difference
analogue, $\nabla f= f(x)-f(x-1)$. From the point of view of analysis one of
its most important properties is that it describes the asymptotics of one
dimensional quantum states in Bargmann quantization.
