Formulaire Des Mathematiques

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.3 lim(a^)*'l \n = ^lini-lf-'ilogaf/iil \n, N^j \ EULER PetrA. a.l777 t.l j î EiSENSTEiN JfM. al 844 t.27 p.51 : ««'» = l_^logrt+3^— ^ +4^^-p +etc.
und dièses Résultat gilt von «^— 1-=0,6922... (excl.) bis a=l (incl.) . | Np ^^ 3-i r/£0.3 lim J[Num(Np^2-;0 —:i/log'{2-n)]Xn\'{a+/2)\ \u =0 I Jensen AM. a. 1899 t.22 p.364 | •2 ns'N^ .]3- limj [Num Np'^ l-x]/x—:i[r\/{loga^'"'' \r,0-u] j(logïx?)" '' |j' = {)i+\y.
j TCHEBYCHEF JdM. a.l848 1. 17 p.384 | D ^ 4-1 xs(^ .3. D(log, Q, X) = /x [ D(log',Q,.x
...) =: lim ![log(oc-|-/0 — log.x]//? |/?., Q— .t, 0| = lim| [log{l-\-hlx)]lh » » » =r jx X lim} ]og(l-\-hlx)[^{xlh) » » » = jx ] •1 i as Q-d . xsQ, .3- D("Log;5? [.t, Q, «■) = "Log e /x •2 rteQ, . xsq .3- L)(«''|^*, q, ^) = rt'loga •21 Hp -2 . vieNj .]3- D" («'" 1^ , q , ^^') = «''(logrO" •3 xsq . ns-N, .3 D"(log , Q, x) = {-l)"-\n-l)\ x'" •4 xsQ . tzeNj .3- D"(log^/a.' 1^, Q, x) = {-irn\x-"'-'[l-l/{l-n)\ S ^^ 5-1 a,bsQ, . a

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