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A powerful method is presented to allow one to quickly set up problems of wave propagation in a turbulent atmosphere and to evaluate the integrals in terms of rapidly converging series. The method allows one to find the phsae and log-amplitude variances, the power spectral density, Strehl ratio and beam profiles. The method of setting up the problem uses filter functions to extract Zernike aberrations, and to incorporate anisoplanatism, and the effects of point and distributed sources. These filter functions can often be cascaded to evaluate the quantities of interest when the effects are present simultaneously. The evaluation of the resulting integral expression uses Mellin transform techniques in multiple complex planes. Keywords: Turbulence, Integrals, Rytov approximation, Mellin transforms, Electromagnetic-wave propagation, Asymptotic series, Gegenbauer polynomials, Multiple complex planes.