50 -^rt. 4. — M. Kuniyeda : 



Then we have a < b, 



since a ^ ^b. 



Let us write — = <7' ?'(«•), 



X 



so that r = - a-"-" &/<i,.^ 



Then r<^0, ;-<! 



since a <b. Now 





and # = gives 



(48) / = 



,'2^r 





From (47) and the above expression for j-, we obtain 



xf C-» {b-a)r, X(t" n^ — {\+b)a', 



Hence (48) becomes -^^ «^ ,y ^', 



or 



-^'[l + e,r)] = « + ^/, 

 b — a 



where e<l as a'-^O. Now x = a is tlie root of this equation, 

 while a; = ^ is that of the equation 



Therefore, by the corollary to Lemma 4, we obtain 

 as ?.-^y: . 



T^T / \ ^^'i^AYi"-) a-\-\ / N 



Now fW = -;,èi%f~'-TT6'''"^' 



* Observe that >0 and 0,>O, which follow from the assumption p >0 and t >0. 



