what is the fourier transform of exp(-a*x^n) where a is a constant and n is an integer

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I need help finding the fourier transform of this function, particularly because I am working with zernike polynomials so I need to find the Fourier transform of exp(-C0*Z0-C1Z1-...CNZn) where C are coefficients and Z are Zernike Polynomials that can be expressed in either cartesian or spherical coordinates defined over a circle of unit radius