On the Intensity at the Focal Point of a Telescope. 267 



_MI f*^a cob *)"«-* 



(2n + l)|h * | 2^-l | 4n + 3-2p J_ sin - lr/a V 



2/7-1 



= 2 W P= y +1 1 4^ + 2 P 4w+2 



1 |4n + 3-2/J 



(2n + l)|* ,f, |2« 



x 



/ r \2/>/ r 2 \2n+l-p 2/>-l 



2n + l " |n p J | 2p-l | 4ft + 3=2? 



/ 2m+l \ / 2p + l\ 



2p ^2„+i- P x> (iY |2n+i-^ , v 2 ; v 2 ; 



W w =o ^ a ' | m | 2n+l-p-m 2r(m+p + l) 



Rearranging the terms so as to collect together the coeffi- 

 cients of like powers of -, this expression may be written 



q 4 * +2 (^r^+YrV P9 f / i\ q l 4n + 2 



2/i+l' \n p fi ^ a ' «*-* l 2^-2g-l [ 4n + 3-2^ + 2^ 



/ 2y + l \ / 2p-2y + l \ 

 |2n+l— p + y . H 2 / V 2 / 



a 4 * +2 (i/3)* p=2 " +1 fr yp_| 2w + 1 2 2 ° , 1 y 



-,V-2n + l' In ~, W |£|2»£W«=i»-i 



I2n + i 



Cf) 



using the expression | m + -| to denote 



( ) » + i)(m-i)(m-:])...|.i 

 Now the expression 



r /2?+l 



2 (-!)■ 



[ 2n + j V 2 / 



<z=p-i 



| jp — g — 1 \ 2n + %—p + q + l \q 



