( 398 ) 



so that from (6') follows 



g,= "^"^ , (29) 



The factor c' serves to make the order of the numerator equal 

 to that of the denominator. 



We deduce from (9), (27) and (29) 



3 I 



~- cz^ m F Ax 



or 



1 1 



r/t = —^ — (L- (30) 



(n— 1)FJf,/ 

 For /we find 



^ //2 / ,.//2 



1 



("-1)/^J 

 3 



cm 



n — 1 



Q lF,{lIJ^\j-n,,F.,) - ':^H{F,-F,-F,,J<\)\ = 



I 3 



F^m 



iF,{FI,F,j-n,,F,) - SH{F,-F,-F,,F,,)l 



or, if we put : 



FAII,F„-n,F,)--?>II{F,,F-F,,F.;)^G. . . (31) 



/:=^^)-^ , (32) 



113' ^ ' 



z^F-^H'^ 



where the factor z- takes care that the degree of the denominator is 

 as high as that of the numerator. 



Before passing- on to a discnssion of special equations //=(/{,r) or 

 F{.v,y) = we wnsh to make a few general observations. 



As the functions 



^ = (uv + ^y j 



n = y-''" + <v ( ■ 



satisfv likewise the given differential e(|uation, the eqnalion 



'i = U (^) 

 or 



(33) 



