562 Prof. I. J. Schwatt on the 



and 



K 



2 

 S 2 = 



K+l-2/3 / i /O 1 



2 (-l)W SVlJVftll >c+MM 

 ,3=1 a=0 \ A-» x / 



^ K + l-2/3 / , o IN 



= S(-i)W 2 (-l)V ( a+ £ 'm.t,.,,., 

 ^(- 1 ) v ( a 7 1 ) m «i- 



K+l 



• 2 



The last summation is equal to m K+1 , since if a=£0, 

 Hence 



52 =S(-1)W 2 (-l) a W +/ " U x+1 ^_ tt -m K+1 . (7) 



JS=0 a = \ U I 



Substituting (6) and (7) in (5) we have 



2 K + l-2)3 /«+£— 1\ 



Qi. + i=S(-l)W 2 (-IMIV^-*-' 



/3=0 a = \ a J- / 



K 



2 K + l— 2)3 / i/O 1\ 



+ 2(-l)«i«2 (-l)Vf^ )m K+1 _ 2/5 _ a -m. +1 , 



j3=:0 a = \ / 



Now 



m K+ i_ 2 /3-«~w*+i. • . (8) 



But if a = /3 = ? (9) is equal to 2. Taking into account 

 — m K+ i and remembering that if /c is even - = — - — L 

 (8) becomes 



LVJ k + 1-2/3 Av-J-flX 



Q le+1 = 2 (-l)W 2 (-l)V l^Wi-*-* (10) 



0=0 a=0 \ H / 



which is of the same form as (3). 



