VARIAE CONSIDERATIONES 



CIRCA 

 SERIES HYPERGEOMETRIGAS. 



Audlore 

 I. EVLERO. 



P 



Conue7it. exhib. die 19 Aug. 1776. 



I. 



ropofito hoc produdlo in infinitum excurrente: 



a(a-t-26) (a-f-261(a-4-4&) (a + 4 6l(a4-6 b) (a + 66)(a4-85) ^- _ P_ 

 (a+d)[a + 6) * (a-t-3i'J(a-t-3i') * (a+5 6)(o-f-5 6) * la-(-?6)(a-t-ry) * "" g^' 



conftat efle 



liis integralibus ab jr — o ad x zz: i extenfis ,• vbi notetur il- 

 lius ^produdi membrum indici i refpondens eflfe 



[g -f- ( 2 ; — 2 ) 6] ( g -f- 2 i & ) 

 [a-f-(2 2 — 1)6] [a-t-(2i — 1)6] 



§. 2. lam occafione iflius producfli confideremus fe- 

 quens produdum indefinitum, in quo fa(ftorum numerus £it 

 ~ «, ac ponatur 



a{a-\-ib) {a-h^-b) (a-t-6b) [a -+- (2)1—2) b] — A : ;/, 



fiquidem hoc produdum, ob c & ^ numeros datos, fpedari 

 potefl: tanquam certa fundio ipfius «^ ex eius igitur natura 

 perfpicuum c(l fore 



A : (n -{^ i) — A : n . (a ~{~ 2 71 b), 

 fimilique modo 



A : (« 4- 2) — A : (« 4- i) . [<2 -H (2 7; + 2) ^] , 

 ct ita porro. 



A 2 Hinc 



