Algebraic approximations to some integrals in optics

A method is described for obtaining algebraic approximations to certain integrals that appears to be independent of known methods, such as Taylor, orthonormal functions, Laplace's method, etc. It resembles the numerical technique of product integration. Often the solutions are globally valid over the full range of each parameter. In some cases a trade-off can be performed between the accuracy and the functional complexity of the solution. As examples, specific integrals for estimating extinction from aerosols are resolved. These analytical solutions are applicable to scattering from spheres, spheroids, discs and infinite cylinders.