Applied Mathematics & Information Sciences

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Bessel type functions (BTFs), which are one of the types of exponential type functions (ETFs), are used usually as basis functions in the multi-center atomic and molecular integrals to better understand physical and chemical properties of matter. As a general rule, the most promising approach for the calculation of multi-center integrals appears to be the called the Fourier transform method (FTM) where multi-center integrals are transformed into inverse Fourier integrals. In this approach, basis functions have not simplicity to make mathematical operations, but their Fourier transforms are easier to use. In this work, with the help of FTM and some properties of Bessel functions, we present new mathematical results for the Fourier transform of normalized BTFs in terms of Gegenbauer polynomials and hypergeometric functions. Moreover, we compare mathematical results for new equations in a table and other details of evaluation method are discussed.