Summary
Zusammenfassung Komplexe Zahlen, Stetige Funktionen
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Komplexe Zahlen, Stetige Funktionen
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Extra Cauchy ProduhtWirhaben die Summen
n Ak Bn
obl
Dr Wir bilden den Produkt aus die beiden Summer
An Bn IIoak
o
bi
o to
an.be ao botao.bntao.bzt.i.tao.br
fiirk O
tayobotaiabytaz.bz tAiob
fiirk 1
o
Bis wir bei k n
angekommen Sind
an abotanabit an.bz t an bn
Frage Durfen wir Zwei Uendlichen Reihennach dieses Schema aus
multiplizieren
A co
T an oooo
Ebi
o
CauchyProdukt Seien Cannemound bnnanoreelleorder Komplexe FolgenDannist
Cauchy Produkt der Folgen Can and bn definiert durch
Cn Mlt Cn at abnk Faltungsproduht
0 g ttnk n o
k
co oakboo dobo
H K L E INO o'tai b
Ay a b CiEoa bnia ao.ba
ao.br tai bo
co Cn
Ci HMP
Termaobnergibt das FaltungsprodaktCo
Aobo Aoby Ao b z Aobn aobo Aoba Ct
Cybo ai b i ar b z Ai bn 1 A ibn
Cn ergibt sichaus die Summen
der nten diagonal
Anbo Anby an bz Anbn
A
z Cn
n o
, Stetigheit
f IR IR
x fCX
Definition mit Limes
f X f X ist stetig bei s lim HX f s
x s
A von belden seiten
Hx c
Stetigan 5 0
fcs fCO 1 1 I ex
1 i Unstetig
lim 111 0 f f O I r
X f O f IR IR
von vonuntenUnstetig
unten Hx HX20
fto Hxco
lim fix 1 f 01 1
X bO
von von oben stetig
oben
Stetig vonbeidenSeiten stetig
Halbstetig Nur voneinerSeitestetig
Unstetig vonHeiner Seite stetig
Stetigheit Folgenkriterium
fX Y Stelle S
fX
Folge Xn Mit lim Xn s
n as
8 Xi f xn wiedereineFolge
Xz f Xz
or
of Xn f xn
ep
S ofCs Dat
stetig an s
Folgenkriterium
of ist stetig an der Stelle s wenn H Xn new Xn EX mit lim Xn s
x co
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