  One of the goals of the present paper is to propose an elementary method to
find a general formula for the Fourier transform containing a pair of complex
gamma functions with a monomial sm in terms of Gauss's hypergeometric functions
2F1. We further collect some mathematical results that follow by means of this
transform. Physical applications requiring the expectation values of position
and momentum operators for a quantum system endowed with position-dependent
effective mass are presented.
