Full text: [Allgemeine Analysis] Theoria combinationis observationum erroribus minimis obnoxiae (3. Band)

127 
a6 
i. 
CIECA SERIEM INFINITAM 1-1 CCA- ETC. 
1 l. Y 
(*+«)» = t n F{— n, €. €, —1) 
ubi elementum f) est arbitrarium. 
II. [t-\-u) n (i—u) n — %t n F[—\n, t* jj) 
III. [t-^u) n -\-t n = 2t n F[—n, o>, 2(0, —y) 
denotante co quantitatem infinite parvam. 
IV. —(#—«)*• = 2nt n - l uF{-in+i, —*»+1, f. 
V. ■ (i+ M ) n -i n = «r 1 Mf’(l-?i, 1, 2, — j) 
VI. log(l-fi) = tF{l, 1. 2, —o 
VII. log£| =itF{h l,f, tt) 
VIII. e f = F(l,*, l,|) = 1 + ^(1,*, 2, |) = *, 3, j) etc. 
denotante e basin logarithmorum hyperbolicorum, £ numerum infinite magnum, 
IX. 
denotantibus k' numeros infinite magnos. 
X. e t -e- t =2tF{k,k\h^) 
XI. sin i == tF(k, k\ f, — jlp) 
XII. cos t = F[k, f, — 
XIII. t = sin i. .F(£, 4-, f, sin i 2 ) 
XIV. i = sini, cos i. F[ 1, 1, f, sini 2 ) 
XV. i — tangi. JP(j- f 1, f, — tangi 2 ) 
XVI. sin?« i = M sini. jP(y^-j-A, h sini 2 ) 
XVII. sinwi = Msini. cosi, F[\n-(-1, —£ W_ H» f’ sini 2 ) 
XVIII. sinMi = Msini. cosi”“ 1 ^—£m-1-1, —+ f> —tangi 2 ) 
XIX. sinMi = Msini. cosi“ w_1 F(±n-\-l, + —tangi 2 ) 
XX. cos Mi = F[\n, —\n, 4-, sini 2 ) 
XXI. cos Mi — cosi. F[\n-\-%, —+ h sini 2 ) 
XXII. cosMi= cosi n jP(—4-m, — iw + i, i, —tangi 2 ) 
XXIII. cos Mi = cosr n F(in-\-i, \n, i, —tangi 2 )
	        
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