100 DEVELOPMENT OF A CERTAIN INFINITE DETERMINANT ARISING IN [2 



Each term is of the form 



and the sum 



Now take (35), 32154. Each such element is of the form 



If a" 



where * and s+l are both different from p 1 and p + l, so that s must 

 not be equal to p 2, p 1, p, p + l. 



Hence the sum of all these elements is 



1 



-2)'-<][(y+j>-i)'-<p[(y 



i 



[(y +P ~ 1 Y- <P [y 3 - <[[(y 

 i_ 



[(y +p - 1 ) 3 - <] [(y +J)) 2 - <]"[(y +> + l) 2 ^?] 



1 



- I) 8 - K J ] [(y +p + 1 )' - <p [(y 



This latter sum we find to be 



165^ 160g 6 - 1360g 4 + 2544g 3 - 576 



2 -l 2 -4 :i '-l 2 '-4 22 -9~ 



Substitute for 5, and we get 



/r,c\ 2?" /i 



(35) = - a?VA 



,, , 



* [It was in the reduction of the coefficient of A that the error occurred alluded to M. N., 

 Nov. 1877, p. 45; Works, Vol. i., p. 184. The above is the correct value, bearing the date 

 Aug. 30, 1877.] 



