14 



Art. 4. — M. Kuniyeda 



where a^o and a;*<^<(W as cc->0.* 

 Then, if a^O and a=k—l, 



if a=-l, 



B, = -^-p' ^ (a + l)x-<''+^>^ = (a + l)-^ ; 



X X 



B,=: -xS' = -e„ 



where Si is a function of the same type as 6 and Oi< S. Hence 

 applying Theorem I, we obtain 



( jw (X) = (1) 



(a<-l), 



(a=-l), 



(-l<a<0), 



Avliere 



T{x)=f'p{t)e<'^^^-^. 



Observing that B.2 = pa' = x~^'^'^^^S(x), where 6 is a function of 

 tlie same type as 6 and 6<0, similarly we obtain 



f J'(^)(/) = o(l) ' (a<-l), 



/<•-') (X) ^ i7r^(l/>î) a'(l/yl) e''^'"^ (a = - 1), 



j^'\x) <o ;r(i/;o (ft = 0), 



where 



T{x) = r B (t) e''^'^ ^. 



./ t 



Hence we obtain the following results: 



•Observe that, when a =0, x* -^Q-<(^x<j'-^l. 



