28 O.V THE METHOD OF LEAST SQUARES. 



and generally, 



Now 



,, , _7T 1 . 3. ..271-3 



/W ~2'2.4...27i-2 

 TT 1 . 3. ..271-5 



_ , _ 7T 1 . 3. ..271-7 



and generally, 



"~ '(2w-l-2p). ..(271-3) ' 



Thus 



f^cosuoLda -(11 

 Jo TTWT => r "2 ' 2S=3 " 

 The coeflficient of u* p is 



1.8...(2p-l) 



XJ * " 



1 1.3 



or, 



. _J _ _ 1 _ 

 ^ H 1.2...^ '2 P ' (2n-l-2p)...(2n-3) " 



Let 7i become infinite, this becomes 



/M 1 J_ 

 ^ W l .2...^ (4n) p> 



and we have only to determine what f(ri) then becomes. 

 Now by Wallis's theorem 



2 t 4...2n-2 - 



Therefore jfo = - ( - J when n is infinite, 



