104 BELL SYSTEM TECHNICAL JOURNAL 



Utilizing these initial values we obtain 

 01 = 1.1, 



(?2 = Z.2 + i£l<2l, 



Q*=L 3 +%L 2 Q 1 +liL 1 Q 2 , 



y ^^ L> (n-1, 2, 3. . . ). (9) 



s=o 



From (6) we obtain L[ = e Ro , and from that L[ = e hL *-* 1+Mt ■ 



Since Li is a polynomial in £, and Mo a constant, we must have L[ =»1, 

 Li= =M, M = 0, that is, L x = t, and hence <2i = f- 



ft - 1 

 L; + 1 = V —**„_,!.;+„ (n = l, 2, 3 . . .). (10) 



5 = 



The next set of coefficients can now be deduced, as follows: 

 £i = &-£«+ilfi, 



L 2 = R\, 

 Q 2 =L 2 +%L 1 Q 1 , 



L', = l L 2 (2i + i LiL,> + £ I1Q } + M U 

 Li = t, 

 Qi = t t 



L^U + IP + M,. 



But Mi is a constant, and Li is a polynomial in t. Let 



L2 = C2^ 2 + Cif + C 0l 



it being evident that L 2 is of the second degree. Then 



L' 2 = 2c 2 t+c l . 



