330 BELL SYSTEM TECHNICAL JOURNAL 



case where the argument becomes infinite, formula (310)- — and hence (3.4) — 

 may be advantageously written m the form 



where 



No{X) = V2^exp(-X)/o(X) = \/2^Mo{X), (3.13) 



an extensive table of which has been published.'^ The natural suitabiUty 

 of the function A^o(^) for dealing with large values of A' is evident from 

 the structure of the asymptotic series for No{X), for sufficiently large values 

 of X, which runs as follows:^® 



iVo(X) ~ 1 + jl^ + jl^, + jl^, + . . . , (3.14) 



whence it is evident that 



No{oo) = 1. (3.15) 



For use in Appendix C, it is convenient to define here a function A^i(A") 

 by the equation" 



Ni{X) = V'2^exp(-X)/i(X) - V2^M,{X), (3.16) 



corresponding to (3.13) defining No(X), with Mi(X) defined by (3.11). 

 The asymptotic series for Ni{X), which will be needed in Appendix C, is^^ 



NiiX) -- 1 - 3 

 whence it is evident that 



1 . 0-5) (l -5)(3-7) 1 



.1!8X 2I(8X)2^ 31(8X)» ^ J' ^^ ^ 



Ni{oo) = 1. (3.18) 



When b is very nearly but not exactly equal to unity, so that 



bR" R" R" 



(3.19) 



1-^2 1-62 2(1 - 6) ' 



it is seen from (3.4) that P{R;b) is, to a very close approximation, a function 



15 Ref. 7, pp. 45-72, for X = 10 to 50 by 0.1, 50 to 200 by 1, 200 to 1000 by 10, and 

 for various larger values of X. 



16 Ref. 1, p. 203, with (u, m) defined on p. 198; Ref. 5, p. 366; Ref. 2, p. 58; Ref. 3, p. 

 163, Eq. 84; Ref. 4, pp. 48, 84. 



1^ N i{X) is tabulated along with N^iX) in Ref. 7 already cited in connection with equa- 

 tion (3.13). 



" Ref. 1, p. 203, with {v, m) defined on d. 198; Ref. 5, p. 366; Ref. 2, p. 58; Ref. 3, p. 

 163, Eq. 84. 



