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in venunttir C et Z) ponendo x^-hzpx ^p^ + ^^ rr o , quod 

 cfim fiat vel ff re :=: — ^ + ^ ^""^ > vel li a?= -' p -^ g V^i, 

 in priore 'cafu fit il :=: r 4^ r' V^t , in posteriore 

 j{ — r- r' V^}; unde r 4- r' V=1 = C (^ -}- ^ y~,) 

 + D -^ s' V^i) C-P + ^ Vr-i.) 



Ex aequntione (IL) habemus 



+ P C^^+^P-^P^-^rr ■ ' 5 ,f^,y,y^y^. eandem 



ob raciohenl est ftinctio integra , quare fit ^ U\ 



Ergo U = CE+Fx')S ...... PCx^^^px-hp'^^q-y'^'o 



Si ponimiis ic^-f 2/>x^+/>^-*-(7^=o, atque pro L^ fcribimus 



:\; = — ^ -.^^ ,V^ i exit , 



^/ -^' V:^i :=-E0-$' V^O + FCS-S' V^i) Q^p ^q Vir, V 



atque u^u'Y^i zz E(^sj^' y^-^^'+FO^s' y-^i)Q-p^q vCil^. 



Unde £ _ >r,» + /.) «iF<= j^,fi-+,^ 



Ec (ic porro ornnes determinancuf fractiones parciales us- 



p 

 que sd -^ • P autem determinatur diverGs niodis pro di- 



verfa rafcione vaioris iS** Si S est functio limplex variabi- 

 . . ^ M' ' 



M notac valorem Tlf, in quo pro x fubilicuta esc — n Si 



E S 



