( 389 ) 



t-j 





ln\ r/,(.^•) Lf, 



(y)f{n)dy 



, (1) 



if both sums iippearing here converge. If wc put 



/? = 



!;.v|2+v' 



we tliid 



/^; 



',;-vi'^~+*^'^ V i-?>vi-+'/ 



:'+° 



^/r( = 1 



m 



i;.,I'-^+'7 



^j- 



/(.^) 





1 /V/O^ 



(A:? < 



M a.yX^+l)^ 



A'^ 



ni 



l^et /> now be an integer, satisfying the condition 



1 +(2 + .y)rf^/><(2 + 7)ff+2 (2) 



We tind then, if 



b 



J\x) =jKiP){^c,jj) hill) dy 



n 



and //(ƒ/) is continuous, 



b h b 



ƒ Yv(.v) ,/•(//) dn = \<ii,i) d;i JAr'/'O/.s) A(5) f/| 



" o a 



b b b 



and so the second member of (1) is equal or smaller than 



< 



I 



Affm^\X\i'- '^+'/V— 1 .^_ 





The sum appearing here converges according to § '2 of Schmidt's 

 paper on integral C(|iiali(>ns in tlie IMalh. Ann. \ol. 68, whilst from 

 the given suppositions al)out /'(//) follows that the sun» in the first 

 member of (1) is ecpiai to ƒ(/■). Kor ///// /// = x follows therefore 



out of (1) 



