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A research program on the engineering applications of light-scattering has been in progress in the Department of Chemical and Metallurgical Engineering of the University of Michigan. As part of this program it has been found necessary to compute various mathematical functions that occur in the Mie solution for the scattering of electromagnetic radiation by single spheres. The Legendre polynomials arise from many problems in mathematical physics, particularly from those involving the Laplace equation in spherical coordinates.