Fourier transform of hydrogen-type atomic orbitals

Hydrogen-type atomic orbitals (HTOs) are an important type of exponential-type orbital. These orbitals have some mathematical properties and they are used usually in the theoretical atomic and molecular investigations as special functions to figure out analytical expressions. The Fourier transform method is a great way to convert basis functions into the momentum space, because their Fourier transforms are easier to use in mathematical calculations. In this paper, we obtain new and useful mathematical representations for the Fourier transform of HTOs related with Gegenbauer polynomials and hypergeometric functions, by using recurrence relations of Laguerre polynomials, Rayleigh expansion and some properties of normalized HTOs.