270 





consequently 



1 



;,=o V-^«+^/ 



If ?;i and k have a common factor, f - ) = O and in the other 



\k) 



case we shall have 



d\k 

 d\i 



hence 



and 



\k J d\k \k) 



d\m 



f 



, 2nimn ^ v o 2mm). 



« — ; — f 'rn\ ^ — ; — 

 S^ — :2 e k (-\2 Bye k ^ (i{d) 



m=l V k />=0 d I ik 



d\k 

 d\m 



2 fc rm\ 



z:eb, ^ - 



2mm {n-\-'k) 



- \ e * 



2 

 = 2 B, 



/=0 



!^\'V4(A-i)v^, 



according to the theorema of Gauss. Hence we conclude 



1. 



^ 2 B) h 



;,=:0 



By changing the symbols of Legendre everywhere into their opposite 

 values, we find in the same way the relation 



2 



:e c, c' = 0. 



