110 



o) Ponatur CÎ5x = log. x- obtinetur notissima séries, 

 quae - par logarithmum ( i -j- -) ope seiiei infinitae ex- 

 piimitur : 



h) Ponatur x"* = 0x; coefficientes seriei , qua Ax 

 exponitnr, erunt functiones m; atque x in denominatorein 

 abit; coëfficientibus his per F''w, F''''m, F''''''<w notatis, ob- 

 tinetur : 



!î!^^r=r-t)H-ri')^.rm4-(f.7F-m etc. . . . 

 positis m=:2; AC^Xy abit in (2x-t-Ax)Ax; atque si 

 Ax=z: i sumatur, obtinetur factis substitutionibus commo- 

 dis , séries : 



Z = Z . (Z + 1) ^ 2 . î . Z^ . (Z + 1)* 



H-f-::i.z^(z+i)» 



~^.|.Z*.(Z+i)* 



■3 4 

 )-7-S 



2.3.4 



-^^y•f•z^(z^-l)^ 



c) Ponatur 4)x=;sin. x; prodit 



Ax=:îi+o^.itg.x 



^-O^C^-+-|tg.^^-f-|tang/x] 



rt (^)'' . [H tg- ^ H- Il tg-' ^ -^ ff *g-* ^} 



+ a!^^ . [iHô -i- IM tg.^- X ^. ^ tg.4» 4- « tg.'x]. 



