Asymptotic analysis susceptibilities

It is noteworthy that Brown himself resumed [88,89] the studies on A-i and modified the preexponential factor in Eq. (4.132), transforming it into an asymptotic series in ct 1. On the basis of Eq. (4.128), he had constructed an integral recurrence procedure, and evaluated Xj down to terms oc 1/ct10. What we do below, is, in fact, carry on this line of analysis that had not been touched since then. Our method advances Brown s results in two aspects (1) for it is simpler, and (2) it provides not only the eigenvalue but the eigenfunction as well. Possessing only the latter, one is able to obtain theoretical expressions for the directly measurable quantities, that is, the susceptibilities yjk>. 

---