612 



TABLE 1 Values of H^, S, and F; for r > A, -lOOF = 5.04 r" 



(L - l)q 



3r 89 or) ^j- 



-2r^ 



7 -r^ 1 -r^ -r^ 



- e + - e (e -1), (49) 



Remembering that 



_3_ _ _ sin e 3 

 3ri ~ r 39 



_3_ 

 3r 



and with "!'. and h. given by Eqs. (34) and (32), we 

 have, finally. 



(L - l)q = sin 29 



9^2 



-r^ /, 1 

 e ( 1 + — 



for 



, 1 -2r^ 7 -r' 

 L ( ^e --e 



-2r^ 



7 -r- 

 TT e 



r^ + 



and the last member of (49) can be approximated by 

 one eighth of (40). By repeated use of the formula 



; n -r' 

 L{r e 



c" ^[n(n - 4) - (2n - 3)r2]e ^ 



To solve this, let 

 2 



q = — ; 



9Tr^ 



sin 29 • r "k. 



Then Eq. (47) becomes 



(47) 



Lk = k" + ( 2r j k' - k = e ^ [e ^ (r^ + 1) - 1] 



(48) 



where L is the linear operator defined by (48) . 

 It is advantageous to write the right-hand side of 

 (48) as 



for various values of n, we can then find the 

 solution for (48) , and the final result for q is 



sin 26 • Q, 



(50) 



9lT 



with 



e (e - 1) - e 



8r' 



1 . 116 



8 9945 



133 ^1, _ 11 ^5 



95472 42432 



32640 



(51) 



With h, given by (36) and (41) and therefore with 

 hj^ known, (44), (50), and (51) give 



