178 



R. FUJTSAWA. 



Hence tliat part of ^-j f^ wliidi is indcpeiKlent of ex])li('it // is 



r ! clx 

 equal to llie coefficient of //" in 



that if^, in 



TT I TÎJ'^^TÏ?^ 



^]/(-r + /0-/(.r)} , 



^vliere y=fi-c)- 



Thus we ohtsiin 



(52, .X, = ^[(Ay|/(.,. + /„-/(.,)|] 



Tin's form of A',, has been ohtained in a different manner by U. ^leyer.* 

 liertrnnd oives tlie followinii' fcjrm of A',, which is sul)stantiall_y the 

 same as (ol) :** 



r ! ax'' 



where a is to he regarded as constant during ditlerentiation and is 

 afterwards to l)e re]^laced hv //. Again m^dcing use of the form of 

 A',, given hy (.51), Ave get 



r/.r" ~ ,6l r! (If fl.r'' -^ ^Jr—]}\ (If dx" 



/y _J__^ ^7^11 _ . _iv,-i«i^'^ 

 ■^ -^ ;e^,(v-2)! r7//- rjx" '"'^^ ^ -^ (Ifdx''' 



* Glrnnert's Archiv d<'v IMathouiatik, Bd. IX. 

 ** Loe. cit. p. 1 10. 



