and so on, until 



Putting now 



we have 



thus 



207 



—-=ön^ — 2xön + 2. 



da 



1 



(7„ =: 2;c + — 



dX 

 dx 



.ƒ.., 







C being an arbitrary constant. 

 Hence 



^-=2^-^ 2(n-l) (24) 



ÓX 2 (w — 2) 



2a* — 



2.t; 



— e- 



2x -f 



C-/ 



where 



Thus for 



n=l <j(0 = 2,ï 



a; 

 



=ƒ- 



IT^ (C-/) + 2xe^'' 



2x -f 

 n = 2 a^2)— ... 



e^' H^ {C—I) + 6^' 



F, (C— i) + (4a-^— 4)6^" 



(7(3; = 



_ F^ (C— /) + (8.f='-20et;) g^^ 

 ~'i?3{C-7) + (4.f'*-4).--^ 



nz::z 71 OW z= = . 



H,{C—I)^Tn-ie^' 



The following relation holds between three successive functions 7': 

 T„= 2a'7\,_i — 2w7'„^o. 

 as appears fi;om the substitution of the values of o(>') and öC"— ') in 



2n 



(j(") z= 2a; . 



ö(«-i) 



