that 



28 Art. 7. — K. Terazawa : 



From the definition of }S'iv) and 61,^2,^3, it follows immediately 



2aYa 



accordingly 



62 <: !f (î;) <r e^ 



The last inequality shows that the value of v must be one of the 



following: 



(i ) V = ()in + l)w, + (2?/ + d)(o.^ , \ 



(ii) V = {2n+l)(o, + i2N' + -2-d)(o, J ^'' 



where 7i and 71' denote any integers, positive or negative, or zero 

 and d a positive number less than unity. 



To determine the value of m in the formula (66) for the value 

 of V given in (i) of (67), observe that the integral on the left hand 

 side of (66) and the function v/i^ — oj^^(v) change their values 

 continuously^ as 6 varies from (J to 1, wliile m I'emains unchanged 

 during this variation. In the limit as ^->0, - the value of the 

 integi'al is nil and 



and therefore we have 



(i) m = —n'. 



Similarh^ for the value of v given in (ii) of (67), proceeding to the 

 limit ^->0, we find 



(ii) VI = -{n' + l). 

 The value of ^'[v] will l)e ol>tained from 



