CAPUT I.

15

4. Quamobrem habebimus aequales feries in (2) (z), quae, etiam di-vifae per Az debebunt effe inter fe aequales, pro quovis poflibili valoredifferentiae Az, quod eft impoffibiie, quin per (25. g.) fit

A + 2Ez-r3Cz- + 4Dz 5 -l -(- rPz r “* + (r+i') Q z r t ^

hinc 2R \+ 3 CV+ 4 DV , . +

+ Aj z +23 J z +3 cj £ + + + r P J '

1+ z >

:o:

igitur per (28- §.)

2B-(- A=o3C + 2 B=o4D -f- 3 C o

B——|A.Cr= + fA.D”-g A.

Q=-P.-

C r + OQ+rP=;oAdeoque feries in (1) quaefita erit

1 u~l(i+z) ~ A (z— |z 2 +iz’ — %z 4 -\ -

36. Corollarium 1.

2 n + 1 -v

^+rj"* *

Series in (35. §-) inventa femper fubfiftet, quemcunque valorem ha-beat z, pofitivum aut negativum; pro —z loco z erit ergo

l(i — z)=—A(z + iz 5 +fz 3 + -’-z 4 -1-" + ' '

37. Corollarium 2..

Et quia efr 1 (1 -f z) — i(i—z) —1 Q—y) , obtinebimus ex (35.36. §0 fequentem feriem;

, f 1 + z> /” . z 3 z 5 z T z 2 n +1 *\

1 f - 1 — 2 A ( z 4 " — -I-(--h ~ ~ ~ H-i— I • ■

Vi —zs V 3 5 7 2n+iy

38- Corollarium 3.

1 +z

b;

eric z

Si b denotet bafin fyftematis logarithmici, ponaturque —

^ j e t 1 lb“ 1; pro his valoribus obtinebitur ej

b +

(37- §) lequens aequatio:A —

/b-i (b-1) 3 (b-iy Cb—1 7 \

's v b+i + 3C D + I ;3-l- 5 (b + l/ ^7(b+i) 7 Te “V

39. P r 0-