One proceeds by "turning the crank" or "plugging and chugging": insert the approximation formula_13 into formula_7. This results in an equation for formula_15, which, in the general case, can be written in closed form as a sum over integrals over formula_9. Thus, one has obtained the "first-order correction" formula_15 and thus formula_13 is a good approximation to formula_11. It is a good approximation, precisely because the parts that were ignored were of size formula_20. The process can then be repeated, to obtain corrections formula_21, and so on.