i39 



st igitur fe X dx [^^^ — J 



II I 1 I C j 



m -+• I >" m + 2 "" j,2.(m + i) ' 1.2.3.(1714-4) ~i i.3.3.4.(m+4) "' ' * * ' 



Hinc ob aequalitatem utriusque pro /e'x™dx inventi va- 

 loris est : 

 c[i— m-+-m(m— 1) — m(fw— i)(m— 2)-f-....i:m(m— i)(m— 2)....) 



^^ m (m — 1) (m — 2) .... 1 

 -- _i 1 I _i |_ _î î I L- _i I L_ _i f_ 



m+i ' I ' m-t-2 ' 1 .2 *m-|-3 ' 1.2. 3 "m-f-4 ' 1.2.3.4 "m+j ' * * * * ' 



quae igitur séries per terminum finitum habetur. 



Forma fe~''x^dx similiter tractata offert: 

 — ^[ i-t-m-f-m (m— 1) -+-m(m— i)(m— 2)-H.... -*-m(w— 1) (m— 2)....i] 

 -(- m (m — 1) (m — 2) .... 1 



i+ih 



_' .1, , 



m-t-i î*m-(-» ' i.2*m-|-3 1 .2. j *m-}-4 ^~ i .2. j.4 "111+5 



§. 3. Ex generali forma casus spéciales deducimus 

 sequcntes : 



1°. Simm, est ir=î-+-ï . | h- — .ï-h-^^.ï-i unde 



' 1! I ? I.I 4 1.2.3 * 



I — I I _i L I _l_ __'__ I .4.., L I _i_ 



2 I*î^^i.2'4'^i.2.3'5^^i.a.3.4*S"T" 



Occurrit haec séries dudum nota in Euleri introductione 

 in Anal. Inf., sed ex alio principio derivata. 



2°. Sit mm 2, eritque generalis séries istius formae: 

 G-2=:î-f-î i4__L.i4._!_ i4._i_ i-l^ hinc 



' Iy4 ' i.a y ' 1.2.3 * 1.2.3.4 7 ' 



C — (ou^i'j — I z _,jj_ j _x_ _>_ I ' I _4_ . 



V- r-3^ — I.4-h,.3- j^«.a.3 -6+ ..2-.3.4' 7^^"*-* : 



18 ♦ 



