From 53a55eac575065055e23bfd52b5d42db7193099c Mon Sep 17 00:00:00 2001 From: flavis Date: Sun, 15 Dec 2019 23:01:00 +0100 Subject: [PATCH] fix wrong symbol --- ws2019/ana/lectures/analysis.pdf | Bin 386949 -> 386939 bytes ws2019/ana/lectures/analysis14.tex | 2 +- 2 files changed, 1 insertion(+), 1 deletion(-) diff --git a/ws2019/ana/lectures/analysis.pdf b/ws2019/ana/lectures/analysis.pdf index e539f5c36a487486b76ae03d4513389abc839120..c75aee84fc45ef6827abff8ce3d63211c4d50f88 100644 GIT binary patch delta 5241 zcmV-<6o%`C&lmg77l5<@@Ad&Pld&o&ml*c}8h=t8TboMR-Unqx%QPuU(Gk0p#w^pdUW*aCCg5)_GosR(d_5FACC4OJyR-k#A&XxqxYHQ zMDffrLA1+`PO`T%csI`(rF8ak&h6~{da=2^Tr58)}uMM$BFx9UMLX`NhHWqxo+~zw8|x?fq+y!TK~~)p`^ppfdaYZ13%F zG&_Mm{gP24oXtM@foGW%jtB#9*V*g6ztuaaUZWWebD6e`a4UwUgwa$G$K;eb9kZFS zk~o-PP)tjd5gj=}?J!Sb&OlE5y!t*$rhk~qE*IJRG0{MQI19BqQXtHw9ovNly?sd? z*q7qOT9z5ZiIl9cuorW|XXlrf=j-E3uox@A=9D1bSlTl_dd5O?wSvHS_=}(D9aVG* zKUnlt_=*g^!W5BCRbR0<6h^R6Mp(Tba9a)tr!d3{TMgjF062tZfFqJsfB&(ZAb%8_ zQGdAQh|}fzx)@}`F@_jw!mTYnU*JnZVh*+h{u+yHqb*UxgSl9xC74KLnm7X+@;fuq zX5jK5T{)JP3z}et)a4@wzm}h^Ub7N=m7DAnJ2ZLE7B2DcR#T(lu3%A)e zgzyk@E;JD=%NcxzAJrx_ZbO!E&3`7_(C5T{Es@O(JvKz^y}s%*BE5|f^&1eVfV#H4 zv1YZCZOyhO(L^_9|1=>C3S0|A2hWBvNi-GZ;i&L%Mo)(W7IHiJbT-M;G15#voi~Zo z@$aeu%d5oMXhWEhV1@<&NpE*To74$88y%2$xc$^ru&}DfF3J%!@Ndw)aDVWV0XX!n zX9+~vJQ!0g)iqHr01tU^9I$q7VU!MR1wR8AvnB0#Qhf%}IwAT8K2Ge=603@31&?7>>^e(yp)@f_uzE4bm@5FtipEGX(wDY%NqRGGwG{ma}nd#V4_BMwFX3yRUBQFzs z5C%f39b=Y!Yi1cMnl-2V=K|eQD=|#wT%$0qdPtvc2c9U0BZ3YyC4|proiApd_#5X* z%MpNc%`QHtY|k}3dwySs=$4EUzq3ecw{T0O~D>{n069WPf(*Bm|aVqiTq zk=u1*nte!l#5YuLLinZxqtuu^ZG7jUYv~3b=J7=_eH$y(O{4@Ow{0AJSQp82=R`VHv22UTXbfU zPoG!V-4*-Jme=V7mIqP{rrTmNUB;?!!n<-O2#+Y?7JvLJ?F7a>0RFXu_JRF^VOR_~ zXCM>p)5Ru9cARP}BaK0B0*5ny2)5Gd5gSP?cbTHb``KVaQWL{P*^UgSP`)Riu=WKU zeP9Z-bzQef6H`!#Ihx&R3hbx?)!up|MW0@0MSSN?qh1>3+r>ero^dsM={u^|@Y`&$ zxt+7wrGJ0xoA#-iSGy&T4Rm1*p>m}C3sjndO-<~dOD#Rg+hzYe5Hswb8;E-_?Zo!E zuo?)|ZrkVg*I#edDd~0Vf=BV;%~^4s;{-2! z;0FgA9CnRAJ}rTzn%Qc7vpK!GxY?|dk_2KR+*kBrMz{}ln^24sR6uRtKOQPKqA#4s&-Uy9J2BFkc z?V{z?#d5I*WPrm5cvT5t(Gakk^G8QH_)CdrDvnU{QdA#<(+Sp{YHnIc3(q*d{ zQy^+cjv1LL8(J?D2vwHJ0C=PpF+7EKLt)SUR@)YkgItn=?Ajw>Gj&WPINof4a4&$Q z7&S;0#<(6ZN|!P)Wt`r%*9i#h!#+f~Y&1O2dEyhAmV~`+su5 zX(v9~AU zA%~zK*4&^OW`}A5J5;0WP=-~BRWbrdE2F|plSE+dq+FRZftkGMplx2zJAb^M!l*4v z_hl$)tTt7r1-BJJrAzR%Y_+l=lZmpJh;u{kVw}%ms1xleTMh1@CE|-cnZj_&u~H!i zNC3>C04iaFoDZT0q@|9xXh75ruco5tEv2;UB*2Ebdk^(9EsK(HtB#34ylW2pIFAMDXxiD zQw93^m@5B**tNM#gM$=jZ?Z+zzn1V>9w0Y!L)W+l13BzmnXy3RAfoW8ft(vnn3B5< z#t9B=BUpUdmL zpVxc%Li>W@*O$=&0w6(Nui@9z#o40n5&q@o>I$ov$EWa@a@g5Bq4nvyD0Y4zlj`jF z;IQx|4+#lyx6od&Mmt!MF`%m^DJ^ZFmh$+tmofqZWC%^H0htA*;!c;I0s);WO49wOay`dTS810A>};)iwVBlzKp2bk4uJgDD0b|1JdeWqTJH~*~9Wce{8BM zSZ)^{=o_>U)l(j5BDoY`pEWk3)N#lX1oJcoimk3aBz#n$@dr+@h5ra(7hH;Q9~Ize z{BBEtN-g74B9`{s3?f$TCv+BuE>?uDme)k~%EM>TzGB$wkQc10`to^rp+x{1p^xN% zuBgGOJ%_R9HB5>J0)Z`g>nnfzQIV7_K$R6wF7v|FG+;1<1BqT)ItsD^h7V%S9iQRN zwxz$u;ctN4Y)oct(pNr5h`7a(sdrW3UqbzJ0M)d^H7(@BcnxbySye z9RU-Ef&>DGf&>GHf&>J&f&>NUz6UijGcYhQIhSz51sn%8GBYqRF*&!B!vzN%Q9?O4 zL^e1=IWadmMKwb;Ge$W#HaA2uG(|KqLNGZwH9jCbLOC}?HaJ2#F*i9yHA6KsMmaY& zH$*WsMKm!&FgZCjK3xhgOl59obZ8(kI5w9dJpn0yCDwa(x+gO`xi%2N+HfB$rkZO^T4AnA|Dk8ZVMdL*#ZuDT>hN^Z4ie zI?p-Z^F8PL{XXC49LI5-CmzS~r<3la2NB|k;}myr zDv;-YNGX!Yt3KitCm`3F6eBU@8InMnut^~jAWl%0wTmUqND_(XRo>w*EKcwQHt`oB zesLml?2bkZ`;b6VRGjEdcA*8s;-r{3iM#CHlB9$bJVrcCWL}s+HCYCDAL>44lXvvi%lDo`8o8lHCc{ZJX zd&v}$?eP}2Capvc##r|jwjrq^XMVFLZAqHQ4cEfAU1v8zCnr66u6i2oKOECEg51I@;P z#Eu}TH)!6N{0Cax1Ic?q%4*PZBxuzEv`(-GWs)q?lk_6J#gm$fCT(Vbv;&}BDY6T+ z9|k(`xg9TqPEnxq8=%W#(DfaV9ss((2zv0587DwyYmhY<^qdcReFA!)2YqgTgMMYf zOI<+rOz`p|(EkD$z$OD@z@S&atE0i-&ET~&V8}%<^Z^+52)q#vhPMDCCV`QwZGe3_ z#Wv3(zP+J#BZ3!3ey*glj-f}R%I#`ei7IMiJv8xaM1v%@%N7cZ`v%unoV96!0 zv>#YD1>}0c@}poyP4GD{eDNVz$(32fnOx21u3-mjCxfrj!8+cXmk8GP1sl48jePFc z>%cdkf=$Q4=3^j#AJ}pSY~^}vn+vvclsf~-Ik3AC*u&h|y8(QUV(r;~*TW`^HPJ0W zSPtDF@$8?7s|Rj@gBvMD&_CrtU%%#zc* z_Y4PfmRWL+DRBNLP*4(F7yvH504}`@e&t}U6a&9;jjl$6YwYxTXK;h_cawX;T?uZn zzu)_S+r7XY?vy|3fbc5BvLa@SA)>?B-|N`oI-H9)A|8w!2u4i>qp^Q=%vLae_6P7La$Mg+E!J_{!1%FX zLOU>#6EP9{Qr|}H)Jem^WRwS;!V6PSrF1HjW?D9wj(pa4P_uOgnOP3ZiUqS#Hg(Pf z@Gk0s&b<%jaV_630p=G13s5(7VHn}^EMorUu!9_YV)UaX;A4(_@eZ(rk6g+TE#rtj zmfz38hLme+Ke7_gi@NTXw%S2W(@L?VO<<-+`UX*xjYUo{C`a^8}?u zzpnxIF&+0aPYkn*v5OrJ+r`s}y68>qqRYZ?}a2bzs&m7};e`J~+N6FO_+y*D{ zG1OBW>gh7z=QMEUHE@@}(E>>D7xvz$KIs{S^gNFEbslth9%R z5&p=z;i6X^T)2kvuh*x88>pRnld0lzvTt!m-Hx=|Y7qY1xe=mw4%@k!;tjSx9=Dcw zvlrS@QKWdM7uZphc(?pvN43R!ce5SU5nrhtc2rk&eTboMR-Unqx%QPuU(Gk0p#w^pdUW{u70XU8_h@#K(d_5F9}f2(JyR-k#A&Xx!w;F{ zMDffrLA1*bkF$3(csI`(rF8ac&h6~%YO%SwSS&v-Ht?~PRLNT3tFqdh|2)ANrN*GNAaZFB`(=nSF zD~W>%2F0{Q8PSmw)DH6`<_zS-&#UjFWPggO>|&997!wT?h_g_;BL%`-+Ob_|(A$^P zfqf}XtYw)ooJh$E3wtpae0Fwmakf6X0E@8#Y)%Q{jio)~qh~BMS1SmNhrjrV-cv=F z@PkEPg|EoqD@+mTRP_~$Ltz99WrWr10XOA_<2Gao*MDrX4Sh-M*Am&x&|^ci-s|f=BhuR#QNIC!3aD$# z8*5fO+16}p5>0et_D>VSpun{-bnt8#lSETd9*znRXY_P9U?I1YPiK=n9V5-;(|MaX z9sjNxu)Iv1jW&cC31(;jko0yZv`L+iv(W*0hucq01q-Ws?4le&1OEoy3x5Yc8Gu9I zdX_+x&4V%3Qe6|}0`QOr#{p~S7Dnm7R`4@`FvY z69UHrOhVWO*Ar65TNWMbK!0%8+Xji2>NLdeJf3LsAv_$3zRrp6c9)S?N+P+7wz(q?WP{Fis4hmi2^#MkFB#f0hXFGg!}5(cp0pLDV#~YQcf;!C~YQ zL{TLg{IK}ESYA$Im=YYv*fEA_dkJPgX9A*X-g;%Jy8tvwufzuN^V`@`kNFlDFF@#|)Ut%*w>RW*B5GnaOn+^wm3ztE0^9A&Z$)I` z_mC#POyQTaL>p1US6LAJ``n7z*?N6>^YI(LvC4HDHGRSh& zAlWo6vdL1F704f(7@IhFWK`{{3L8E+$pBPj``}a@LR77*&C%~zZU0#8`=`ZwD&%H~ zTTi8K76P$U$$$O#pVxOO^WtQLuCvB{zc1otj|PLRVWI|a<2gxzMu=x*;t)NX&@;s~ zZ_TgSE(~UCPd6|qj%8b4Hen%i%4cnV4D!wL}L(>s{>8hR?YXblA0JU%64Qph4MWCg|#o> z=mS%rt?Rl?nwWw@%+c&tQ(#9GsP@(yDf;v}E8;tE8uijJ-!2Y1^^B|8E8kJQg5PF~ z&CQ(6E`R)6-?UHFyxJ{!Y@iEk2$du4U!c+yY-(cvTx#h_-Y)y+ftX?c+(6ueX(zVN zh1EcycH2I`yZ(B+=Tf1=*y7Y9Zdi5CB^fG60bQi5rWOawO-Zj?7d(m&uTP8X9LIR! z13x&};IJ$F@p%a>)y!7w>&?mK`SoU%jC{@!(|?4ln^er#0#g9MCm9Dm*@+6lpwUo0 z-g?K%h2PY1sl~-b^})6GnUaNf@jYh}CS@39!FHUAYv54@8W3Is!$dkyBE19*3dZz=3_+}s!#5`QXk{c-ot0&6?dNPgtajfq8xM;O-r63ta0sw|f z?eKx>)Pc6RE_1i?p|+g5sSkHo!3NW4172>+$y?Uatt^Dr0>DaT*IE+oo(N%cqX9h? zCK)h+soF)$%k$-84afk85AdoIz@i~wH-G1kj&ktj9H>Sj?u=JIImfwi&8Xl-N% zf~Ct=F{Z%gB*%=*lnt#{34|)kWB@!;ix{3lyP>dWf2(Z^$U!biL3ZsCu$ek05*%+f zK)4q`Qj8j;J77_^j;%iKMKabiX>bOvr-}Mq5~!qN_*1ADtYS~XEjgScyE!HY(0<90m z+@2juJwgsaL9Dq!Gt3Uv1a_!K*`W-p602kckXA;8nI?(A+)24IX96>M(SJePyr6e@ zJ%v$QmhQ_?(pYV(P77`;f=ZX*Y1wLJK_(MrF%gS`+{HMb!%!#MQ??r1K}*CJdoqRL zlw+kr4v+wtLjhF6200%@4@gTLZ_$9L8(vLC(OXJs*UQty0hSl8LUY(8i*zAh=xJnN z5+BTSd3|1tb4AHqR98-|0Dp@yy2TlyUOi!OEYg!9Kj=K6FE|pdIc(Aa8yr#>(>}3` zSyNmSt)>d}^(j^U1+i;$nFa?b&fa8;s(&rvvphg<=7z3u4F+=9xiVvc$U#KmQv*2% z+Rv2SZ6I&Ni~_myk1R|LaC-s|>({LcF84dh(ogG1%hcm|mY$SEveh(R*1^aExn{?n<_hpm-?f zkBbCq0urbPg#>CG2{hE#K!W3C7XbQe7L@2lD-YfO*%$zrdjtSA1pw4U0C+kP065;% zPd}H}dq1!D@P+mT!~2)a0RkW)TCd^Plf~(x?h*dw`tlO1m`5k@mvY$Yd!hBox+r#j zB$o{W0v-bBq?auM0%QnDtO1z?rQ%kXnF0bQ0Z5m@0s<8Qsh8IR0z-db%Ra}Ji0JhO z4hFz<#~YM?FnQQgIeZ1{%A?)@0iU3@ZnFk9V=k^#-?m|5PlvLO+Bo4t|b_An<=nh{+Nf)_?9ohJdJ^3t7{Jl z9~Ef)ffH=uKLXeVmtx#U1vnbN-4dWu%lMRtrTsR8h*kRuorR%`6``x;HIcpY@L9Bb z3|k%Yf^}72J`XRn2tXtBksQz!H8{2BF!sELN%24+uqAJO?Qc>)lClM;vf{~QUYME& z42EzZ(JMI%6FV>2$rhxJN9}(kqM3-?L0TYLO1OkVA1OtbB1O&Hy1O?~52Qx7^FgG+amukZW z90xNoI50OfGq;Vy1qU2bGc`0pGetu%FhVvpGcYkhHaImyL_tD1MKLinFhevnJ|H|Z zH8eppMME$!LN+xsFfl22Sc&*Pu>>pbUt&-a|~_xpUGa~#KU9(o+d-<5PD-H8xK9H+E{Blj8d6sann z5hv|j5}PRTh$EqP?nzRSlqCtg>LXrp0&=Z?NhuOTN|1Qclue3}0C9q{tz8q+oFtMs zUgaJB;^G94VH5vj#4k?R0=uIT!`>v2loTg=i(P2Jurw(pPQnhm_i<82ob)vo@^$?| z;&dNiVR=$coW9W(azy?L;tcL*VI}f}IHT@c_sI-7a(`uUrbbzlU{Xb#`7^CaV}@0K zNr*Vh^X*(L!|J4(IC(ehHcqj>hB!O2EPR^O6zAYbyCa1mm%<+^PGNOx@+_$(&M#{% ztWCnixz)zPa8gH{2WKsOp424~B7q0(TzyhcB=}u>MoWf~q=86yO>5GSM2WO#WRt&9OyvXDOvcaa)Z!ei5QV?fhYtl;OK#X;7VH!ylId#RFv?1vtMXrVINL!J+KU(-4 zX)hk{SPL^q2k``1fBsISqj*A!tou}kT}Wr~L_Dx2nc|7*<%p+o3TWab>p|0hlXH)ERs!nke;NMcv9P= zN!m=1egw3wMD~JqBS3pT_qigF5d}Jq1f6n0=NX`DNzkn~=*~xG{sgkxf$Y~oj}Jl5 zPeHFsp!c7kZwPoH6Xd)PUR(@+`dtD2+2rMTFkmnkI2sHp0I!?}gRg=i4tPz$>vh1; zR50v4Fg(u&*oRYW^DN@q{iv#V2rG^2B`hdz0Aa~+i;HJmytVTa76rE?2^7!xn&^4L zJ76N`bkc1wna`b)1*T2{(*}X*wZM!FFq4b-el(c18q5v{bNYa}T(Wt8>}vi)uwW}# zSQ{*w1r{#?A6)}WUII&}fLs(%&$1I>d3~^g7gjC-tGF_&Ig_99xog?M=aa#@Y_Oj9 zZfFVe`h$(ngH3$y7n{N6m0(LD*m@G=9|GI%g0Hw9+vkD;j`Ewb@XWv9z-G2uh;K&aql7GM<-g|fxIPx_($^|{fAsqh?eE%Cb zkql0jAx!x~W=SFMJ;lMCW|o{`3Y)Z?OI&g#i{niiM%mKH!Q+{s*Znpq;*ufth!k^q*clnHezZ!$T+223BdM^mv z4+H;l4?Y+J{+k9KqOm%dFqOl=a~gOb2fj8S08i6m8*To|5q>M&3Zlh-#|1wgu8(yB zfl9W6()BivW*5-)n%m?B7Km=Ax>!I9eeXN!? z;F~u10Yr`mQNuw)_7{!J(MAkoj)Nvx8Eu*dVzCq&w;#kKRkYb-moMv{8cbwDtH6?S4ZvyZyp72 zA;uCHu`l%<)J}c(O)w7SLC5pLcvLB!z@(Wt08BzY>wBo# zI+;wV3Z^y((@-{b`UEfo^+0Dn0JFH3A5;Ld1Hl~B4V@cCxIFWie+$^b0(@e0VFFmh zkuUxhe8fjC;fR)UM4xaRxvRi3Y#F*+u5XmGxYTV z@C`F|XJxRf2H0JfptR_o2(XvwxQ}_dA2nOQW8;IU<9g`PuVgjCKP|V0=wUA75$>6z z9PcrIrrB|nT>XLD-~>K~dXhsetO9=O08R}Br}2T*Gt7;%%<-R@-se!h^gKSjdSMv2 zh%%y=P(bw;rsL&x_VAj7KXPuU=+yvRxQ6ntzfK25sGWM9sp4|7Z*WK5jI`To5&qn{ zVWPLbw{x|{8=PcEb;O&q$d1CrJL$3=MTmEC+h2B6SG;!$?5Ljj%6@A{^~D!6#Eu$> zFK2=sMT&3SqYpup_*QuBsG<1s?a$JUCj5;M1& diff --git a/ws2019/ana/lectures/analysis14.tex b/ws2019/ana/lectures/analysis14.tex index 21c1b99..76e8576 100644 --- a/ws2019/ana/lectures/analysis14.tex +++ b/ws2019/ana/lectures/analysis14.tex @@ -305,7 +305,7 @@ Kostina glaubt, dass das so stimmt, aber offensichtlich ist sie sich nicht siche definiert durch \[ \sum_{n=0}^{\infty} a_n (z - z_0)^{n}, z \in \mathbb{C} - .\] $a_n \in \mathbb{C}, \forall n \in N_0$ + .\] $a_n \in \mathbb{C}, \forall n \in \N_0$ \end{definition} \begin{bsp}[Exponentialreihe]