178 Miss Dorothy Wrinch on a Generalized 



Now it has been established * that 



i U U 2 » -n/f \ i cc(a-l) 



JH-al+a.J-fa v if 



- \e u ir a --, p., . -,, ^ --p 5— 3... ]r(l + a) 



L iu.u 1 (a — 1) . ?/- la — 2.?r J v 



i£ ! argw | < 7r, 2^~ a being interpreted as e~ a lo s w , log?/ haying- 

 its imaginary part between +iir. 



It remains to choose the correct hypothesis for the 

 asymptotic expansion of qF 7 i-i{z) and to prove its correctness 

 by induction. 



The relevant data are 



(1) If |s| is large and large] <7r, 

 J.W - (^)*[oos(#-imr-4») [1 + 5+-] 



-shn.-i^-i^g-^...]] 



•i{z-ls 3 ) 



where s 2 = n + ^. 



(2) If [^1 is large, 

 F 3 (l+ai, l + « 2 , l+-«s ; ~) 



2 5 V' 2 L' 



+ e +te g -|r(*i+.«2+«3+3/2) ^-4«^+?(*:-f * 2 + *3+3/2)-| 



_ n + ai rn-a 2 ri + a3 -' 



(2tt) 32 i/4 



2 4 



r g 4^ + e 4«/ 



1 7TIS 4 



e ~* 



1 . TTZS 4 



n 



* Barnes, loc. cit. 



