Procedure for Obtaining an Algebraic Approximation to Certain Integrals

摘要

We have found a method for obtaining algebraic approximations to certainintegrals that appear to be independent of known methods, such as Taylor, orthonormal functions, Laplaces method, etc. This method has the advantage of sometimes producing much more compact forms of the integral. It often gives results where the others may fail and in many cases the solutions are globally valid over the full range of each parameter. It sometimes allows for a trade-off between the accuracy and the functional complexity of the solution. Specific problems in the estimation of extinction from obscurants and other aerosols are for the first time completely resolved analytically. These analytical solutions are applicable to infrared and millimeter wave smokes as well as biological and natural aerosols.