92 DEVELOPMENT OF A CERTAIN INFINITE DETERMINANT ARISING IN [2 

 Again 



'y+p+l+K y+p + K' 

 1 



~ y +p + 1 - K y +p K ' 

 Hence we have 



\ / 4 4 



' ' = ' 



_ 

 4* 2 (2* - iy 



a 4 a 4 } 



l) 2 J 



f_a 4 (4K 8 + 6/c+l) ft 4 (4* 2 - 6<c+ 1) 

 h \ 4K 3 (2/c+l) 3 4/c 3 (2/c-l) ; 



f a 4 (4/r + 6K+l) _ 4 (4/c 2 -6K+l)1 _1 



t | j * / " . , \ j /- -i \i I ** / , 



I 4 ' 



or 



S (p, p) 3 / . 2 , \ j 2 T V j + ^ ; 



_ 

 2/c 3 (4K 2 -l) :1 (_ 



which agrees with the result of p. 89. 



[This method was employed throughout. The details of the subsequent 

 work will not generally be given. 



To find the terms of the sixth order in a or q lt or of the twelfth 

 order in m, we must find the sum of the products of the quantities (p) 

 three together, no quantity (p) being multiplied either by itself or by a 

 consecutive quantity, that is to say we require 



-S.(p, q, r)-2(p, p+l)2(2>) + 2(p 



+ 2(p-l, p, 



where p, q, r are all different, and therefore 



We have 



