170 Miss Dorothy Wrinch on an Asymptotic 



The values of </> lie between — it and + 7T ( + 7r not 

 excluded), and the result therefore holds in all cases under 

 consideration, for Stokes's result holds for all integrals of 



I 



the form \ e a dz, when — ir< arga<7r. 

 Similarly, 



.q+^+Y +j+gg , * '(l + i) 



2 ^ _i_ 7t - — ^ 4o 4 e 



6*- 



If <£ = 0, 



+ ^ r (a+/3 + y + £ + 3/2) 4p*« 2 

 X e e 



Hence 



x cos[V-^U + yS + 7 + S + 3/2]. 



Thus if — 7T<^<7T, 



lNl + X N, + 2 N, + 2 N 2 - V^r/>- i(a+/3+r + * +3/2) 



[.-> 



+|3 +y + o+3/2) 4p*e 4 



zb^ r («4-^4-7+^4-3/2) 4p*<? 2 * 

 + e w 6 



-^ r («+/3+7 + ^+3/2) 4pie 2 4 

 + e £ 



+ e 



■7 + ^+3/2) -4p*« 4 1 



according as $ is positive or negative, the last term being 

 omitted if (/> is zero. 



