662 



BELL SYSTEM TECHNICAL JOURNAL 



z = complex quantity, unrestricted. 



2 = conjugate of z. 



2", hv X = exp[Aii? (log z) + in arg 2], where {2x — l)ir < arg z 



^ (2x + l)7r. 

 •^ g<2TMr2M^ br(:v - z)). Branches (:x; + z;), y = 0, ± 1, 



do 2, • • • form a complete set and without repetition 



unless /x is a rational real. 

 oi, /5, 7, 5 = complex quantities, real parts greater than zero. 

 6 = principal argument. — tt < 6 ^ it. 



X, fjL, V = complex quantities, unrestricted. 



p, a, T = complex quantities, real parts not less than zero. 



^n(x) = exp{Trx^)Dx'' exp{— Ittx^) 



= (— 2Tr^)"'Dn{2ir^x) where Dn is the parabolic cylinder 



function of order n 

 = (— 27r^)" exp(— ■Kx'^)Hn{2Tr^x) where Hn is the Hermite 



polynomial of order n. 

 }p{z) = r'(z)/r(s) = logarithmic derivate of the gamma func- 



tion. — t/'(1) = Euler's constant = 0.5772' • •. 

 * marks a pair as being the limit approached by 



regular pairs. 



