(814) 



[n{n-2).. 1] + 2a, [(n -2) (2-4)...l ] + 2V, [(„-4)0^-6) ..1] + 



[(u + 2) (n).. IJ 4-- -^^. [(«) ('' -'^) -IJ + '^'S K'^ 2) («-4) = ...IJ + 



+ 2"-3/2«„_2 zzz O 



[(2« ~3)(2?j-5)...lJ + 2a. [(2;^-5) (2n-7) ..1] + 



+ 2Va(->;i-7)(2n-9)...lJ -f 2a, ^2 L("-2) (,^-4)...! j =. 0. 

 From this il follows thai : 



U„ = .i'" 'V 



n(n-l) H{n-l){n~2)in-3) 



.«" — '^ -l- .r" — ■! — 



. . etc. (20) 



24 2/ 



from which we derive that (/„ and </„ arc solutions of the 

 equations : 



_-" _ 2.1- — " + 2« Un — 



fZ.r' 



(/.^ 





and the recurrent formula becomes : 



2r„4., -2..r,. + ,.r„_i = o 



The .l-coefficients are determined in the same manner as in all 



former cases: 



.+» 



ir-^' 6^„ Un dx =z 



ƒ 



for all \alues of in. different from n so that 



where 



and 



J " 



d-i = r T-^u^,. /:/„c/.6-= ƒ 



/7„ d.i 



2'-' 



2" 



ft;. 



(ln~2 



ft;i— 4 



— etc. 



(27) 



« / 2 V 1 / {n — 2)/ ^ 2 ' . 2./ (n — 4).' 



From the numerical values calcidaled Iw (26) and from the 

 diff. e(|ualion it appears that, but for an arbitrarv constant factor. 

 the (/„-functions are eipuU to the derivatives of the )i^^^ order of </„ 

 or e~-'''' ; we might, thei'efore. write : 



<ƒ „ — Kn 



(/a-» 



