XIV. Approximate formulæ for functions expressed as definite integrals

Abstract

In the theory of absorption of radiation in an exponential atmosphere it is necessary to consider the integrals The available series-expressions for these integrals are inconvenient for numerical calculation for moderate (integer) values of n, and for values of t that are neither small nor large (say from 1 to 5). Approximate expressions E′ _n (t) and B′ _n (t) are therefore given here, in the form of finite series (or index-sums) four or five terms suffice to give a good approximation over a considerable range of n and t.