143 



hoc est (extensuni ab x nz o ad xrzi) 



-— _! 1 I __i_ 4_ _L _L I J I l L. 



3.4.5 '^ î * 4 -5 -6 "^ 1.1*5. 6. 7"^ 1.2.3 6.7.8 ^^ • • • *^ 



]iabcbimus : 



"7 ^ (9 -f- 5.4.5) î • 4.5.6 ' 77^ • FT"6^ ~^ 1.2.3 ' ■6".'7~8 ~T~ • • • • 



Ex his aiitcm certeni cst^ habeii generaliter summam se- 

 rieiTim istius formae : 



I • (m-h2)(m-hi)(,m-h^) i . j ' (m-h3)(ni4-4)(m-t-53 1.2.3' (.■m-i-^Xm-\-s){m-h6) 



vel etiam : 



1 ■ (ni-h2)(m4-3)(mH--4)(mH-5) "^ i . 2 (m -f- 3) (m -H 4) C»^ -HiJ (w -|- 6) 



4- 

 vel adeo 



.j L_ L_ L 



^^ 1.2.3 • (m + 4j(nH-53(m-f-6)(m+7) "^ 



+ A. 



I * (7n-f-2)('n-)-3)(7n-f-4)(m-f-5)(m+6) ' 1.2 * (m-)-3)(TO-J-4)(m-t-5)(7n+6)(m+7) 



etc. 



H L_ . 



' 1.2.3 (Trt-(-4)('^+0('" + 6)(wi-f-7)(m + 8) 



Quarum igitur serierum smnmae pendent ab integralibus : 

 fdxfdxfdxfe'x^dx, fdxfdxfdxfdxfc''x^dx etc. 



§. 7. Ex superioribus jam directe ad sequentia per- 

 ducimur : Sit dy^=:e''xdx-\-e~'^xdx, unde 

 y =: e*x — e* — e^'^x — e~~* 4- 2 , et 



Sed per scriem repeiietur f(e'xdX'\-c~''xdx) 



— o/'^_i__Jl__- . '^ I f^! L....) et 



\i.» ' 1.2.4 i.a.3.4.6 ' 1.2.3.4.5.6.8 ' ' 



