Opcscula 107 



Qunpropter omnil)iis his seriebus , qiiae quanlllatls cf valo- 

 rem praebent, considcralis, induccmus 



^ >-n— .njn-.1^„(n — 1) j-n-l _|- clc. 4- n (n — 1) (;« — 2) . . . 2.1 ) eY 



2.3.4. .(,,+1) 2.i.4...(«+2) 



3.4.5... (n4-2)r»+5 

 j«_ '^ Li i-f- etc. ; cd iJco 



2.3.4...(n + i) 



~ ^ n-f-1 (r:H-2) 2(^4-3) ^2.3.(«+4) ^ 



4-nC„_-1)...2.1q_«(n— 1)...3.2r±n(n— 1)...4.3J'2_j:„(n_1)...5.4J.3^_^t<,.^^n• 

 Si primus terminus numeraioris hujus expressionis dividatur 

 per denominalorem,priorcs n termini quoti sunt priorcs n ter- 

 mini seriei nolissimae, in quam evolvilur funclio e^, nempe 



y- y^ y4 yS y6 



^ 2 2.3^ 2.3.4 2.3X5^ 2.3.4.5.6 



er20 formula 



'O 



+ „(„_1)(„ — 2)...3.2.1 



^n 



-4-„(„_i) ...2.1 q::n(ra — 1 ) ... 3.2jHr eic. 4-^' 



proxlme exprimil valorem e^ eo pro.\imiorem vero, quo majov 

 est Humerus n . 



§. IV. 



Evolulio inteeralisf- ■ in novas series. 



° -^ log. X 



In hac formula intcgrali ponatur ey loco x, et erit 



/d X redy r dy 

 log. X "^ log. e y -J 14,/og.y 



Supposita serie 



/1 



-= A/og. y+B /og. y" + C /og. y 4- D log. y'4- E /og. y 



4- /og. y 

 '/og.y . 



differentia tione eraergit. 



4-F /og.y 4« etc. 



