268 PROFESSOR K. PEARSON AND MR. L. N. G. FILON 



Before we consider the determinant and its minors, we may note that 



log 



i) logp - 



where the B's are the BERNOULLI numbers. Hence 



and we have the convenient form, 



,., = n log r (p 



' 



p(p- 



JP 



S 



where S is the semi-convergent series B,/2> B. ( /p :t + B.7j> r ' , &c. 

 Now we have at once, 





, c 

 i" 



+ 1 2 (/> + 1) 



Divide all three columns by \j(p 1) ; the first row and first column by y, and 

 then the last row and last column by 1/y ; we find, 



A = 



Divide the second row and column by l/p ; add half the last row to the second, 

 and we find, 



1, 1, -2 



0, (p - 1) S, 



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



