of Cotes*s Theorem, 15 



This equation, in the five particular cases just enumerated, 

 gives 

 1, n = any number, Q = 0, 



I 



In ^ 



2. » = (SW +1) . y. 



f f = /(i+v)".(ii|f. . .{3,3} 



1 



'^^^ ''^' = ''".(i+^')^{^ . . . {«4} 



I « ^ ^ •' 



5. n= (6w+2) .-p. 



f f =''"•("^+^*r•(S)•(lE^:)• .{^,6} 



Our third equation { 3 } » gives immediately 



^' '^ 1— 2«''.cos. nS+g*" 



/O. /O "= (7I7F — • * ' • l^'^l 



1 a 



which, in the abovementioned cases, becomes 



r(^) r(^> 



1. i i_ — (inf!)! . . . Uq] 



r(0 /O^Ci-^')" l'^' ^ 



1 M 



r(^) /^> 



