56 Art. 4.— M. Kuniyeda : 



yfijj) = ^ 



where f {y) Is mi. L-f unction such that if ^ f{y) > {VvY ^-^ ^-^^ > then, 

 for large values of ?^, we have 



ivhere v is a certain function of ?., tending to zero as /^x . 

 Easily we can prove that 



>' > {f {?)}-'"> {W)' 

 as ;.->oo . Hence we liave 



Lemnia 6. Let f{y) he an L-f unction such that 



//>/(?y)>0/?/)* 



as y-^oD . If y = is the root of the equation 



yf(u) = ^^ 



for large values of ?,, then t) can be expressed in tlieform 

 where g is a certain function of the same type as /, namely, 



'f>g{y)>{m' 



as y-^cc . 



As before, write 



f, = rr-" ('Kx), n' = - œ'^'^"^ ('J,(x). 



Then, applying Lemma 6, we arrive at tlie following result. 



Let X < p < xy/a" or (> — Ax[l-Ji{x)}, where ^ > 0, J> > and 

 ^ < I. Then, if b > 0, ive have, for large values of /, 



^C) = 4;.%)i = '^-'■^('•^■ 



