94 DEVELOPMENT OF A CERTAIN INFINITE DETERMINANT ARISING IN [2 

 we have the materials for forming the expression 



2 (p, g, r) - 2 (p, p + 1) 2 (2)) + 2 (p, p, p + 1) + 2 (p - 1, p, p) 



p-l, p, p+l). 



Before doing so, substitute 



B A-+ IT coign A, 

 2(7=2^ 3 + 37rcot qwA* if A. 



Then in the resulting expression, 



.,,_ (j* c li( ( f+l) (Zi' i (35' 2 + 1) 



- -'-, Jg_ jy + 256^"(3 T ^T)' ~ 7683* (3" - 1)' 



y," _<z 



. J .^1 



j "* r cr / _3 / _ 2 



- 1)- 256<f ( 5 2 - I) 2 



= 0, 



</i" ('/+ 1 ) 

 coefficient of ^ = :! - cot ^ - 



y. 6 3y+i) _ /+ig 4 -< 



3 r/ - 1 )' w t q7T 51 2 ? T ( 9 2 - 1 Y 



g. 6 (5 ? 2 -2) 



- 27T " 



3^ ^(^- 



ir q "- 



77 



+ 2 - 3r/ - 1 - 2 ? ' + 2 + 83= - 3] 



= 0, 

 and these supplementary terms of the determinant reduce to 



/ 1 52* -353*+ 8 7T 2 



