(641) 



where 



ap=2{v -\r p), 



(2n-p-l) ...(2«-i» 



p! 



(2/1 — p — 2) . . . (2n — 2p — 1) 



pi 



(n_;, + 1). .(„-2/, + 2) 



p/ 



<V + 1 . . . «n — /J + 1 



71 'i 1 



and h stands for 1 when n is even or for — ^ — wlien » is odd. 



Putting a^, = Ibj, this equation may be written 



22n+iè^«+i V---Vi'«+i/;.+i = -i>« .... (2) 



and it is found that the determinant Z)„ satisfies the condition 



n—\—n—2 

 Dn = nb^ . . b„ Dn-\ ~j b^ . .b„ . b, . . bn^\ -Dn-2 + 



n—2 .n— 3 . ?* — 4 



4 ^7 b^ . .b„ .b^. . bn-[ ./',.. bn-2 Dn-3 — etc. 



tlie last term being 



(- 1)'2 " 'C'^ + 1 V, ■ . b„ .b,.. b„-i ...b,..b„_.b„_B„ . 



+ 2 -+i 



when 11 is an even number, and 



n— 1 

 (_ l)^~ b,..bn.b,.. bn-l ...b^..b,^ D„-^ 



2 2 



when n is odd. 



Substituting in this equation Di, hy their values from (2) we get 

 this second relation between the coefHicients fp 



= 2 



/„+. _ 2^ (- 1)P (^r+T)7— 22..+n,^...,^+,6„_^,+, ...,„+, (^^) 



Finally we will show that from tbe recurrent relation between 

 the determinants Dp the value of 



Lim I / z=. a 



Ï1 = 00 



may be deduced. For the series 

 is converging when 



