

For the evaluation of I. and I,., ve use the following approximation 



f(t) dt a I X (n) f(x (n) ) (59) 



1 i 



where n t are tha setfos of the Laguerre polynomial and \, arc the ' 



* (5) 



corresponding Chrietoffel numbers. In this report, n la taken as 5, and x t 



(5) 



and X are given In Table I. 



Table I: 



Zeros of Laguerre Polynomials and 



Christoffel Numbers 



H x t (5) 



0.2635&03 0.5217556 



1.4134031 1.3936668 



3.5964258 0.0759424 



7.0858100 O.C036I17 



12.640S0O8 0.0000234 



The exponential functions in Equations (47), (52), (53) and (54) are highly 

 oscillatory when the real part of the complex argument is small and the imagi- 

 nary part is large. Oae of complex arguments in Equation (46) can be expressed 



as 



-u (7 - iu-f.) « - k sec 2 • [7 + iR cos(9 + 0)) (60) 



13 



