Commit f633c51e by Michael Kohlhase

### moved

parent b57827b6
 *.log *.aux *.bbl *.blg *.ilg *.idx *.ind *.synctex.gz auto *.thm *.rel *.out *.ltxlog all.pdf all.tex .graph.* *.xml *.omdoc *.sms .nfs* *~
 \begin{modsig}[creators=jusche]{baxterhickersonfunction} \gimport[smglom/numberfields]{integernumbers} \gimport[smglom/numberfields]{natarith} \gimport[smglom/numbers]{cube} \gimport[smglom/numberfields]{positional-number-system} \symiii{Baxter}{Hickerson}{function} \end{modsig}
 \begin{modnl}[creators=miko]{function-zero}{de} \begin{definition} Sei $K$ ein \mtrefi[ring?ring]{Ring}, $\inset{0}K$ seine additive Einheit und $\fun{f}DK$ f"ur eine Menge $D$, dann nennen wir jedes $\inset{z}{\PreImage{f}0}$ eine \defi[zero]{Nullstelle} von $f$. \end{definition} \end{modnl} %%% Local Variables: %%% mode: latex %%% TeX-master: t %%% End:
 \begin{modnl}[creators=miko]{function-zero}{en} \begin{definition} Let $K$ be a \trefi[field]{field}, $\inset{0}K$ its additive unit, and $\fun{f}DK$ for a set $D$, then we call any $\inset{z}{\PreImage{f}0}$ a \defi{zero} of $f$. \end{definition} \end{modnl} %%% Local Variables: %%% mode: latex %%% TeX-master: t %%% End:
 \begin{modsig}[creators=miko]{function-zero} \gimport[smglom/sets]{image} \gimport[smglom/algebra]{field} \symi{zero} \end{modsig} %%% Local Variables: %%% mode: latex %%% TeX-master: t %%% End:
 \begin{modnl}[creators=jusche]{logarithmicintegralbig}{de} \begin{definition} Der \defi[logarithmicintbig]{Integrallogarithmus} $\logarithmicintbig{x}$ ist f"ur alle positiven \mtrefii[realnumbers?real-number]{reellen}{Zahlen} $x > 1$ definiert: $\fundefeq{x}{\logarithmicintbig{x}}{\riemint{t}2x{\frac{1}{\natlog{t}}}}$ \end{definition} \end{modnl}
 \begin{modnl}[creators=jusche]{logarithmicintegralsmall}{de} \begin{definition} Der \defi[logarithmicintsmall]{Integrallogarithmus} $\logarithmicintsmall{x}$ ist f"ur alle positiven \mtrefii[realnumbers?real-number]{reellen}{Zahlen} $x\ne 1$ definiert: $\fundefeq{x}{\logarithmicintsmall{x}}{\riemint{t}0x{\frac{1}{\natlog{t}}}}$ Da die Funktion $\realdivide{1}{\natlog{t}}$ bei $t = 1$ eine Singularit"at besitzt, ist f"ur das Integral f"ur $x > 1$ der Cauchysche Hauptwert zu nehmen: $\logarithmicintsmall{x}= \rightlimfun\varepsilon0{(\realplus {\riemint{t}0{1-\varepsilon}{\frac{1}{\natlog{t}}} , \riemint{t}{1+\varepsilon}x{\frac{1}{\natlog{t}}} } ) }$ \end{definition} \end{modnl}
 \begin{modnl}[creators=jusche]{stonehamnumber}{en} \begin{definition} For \trefi[coprime]{coprime} numbers $\natmmorethan{b,c}1$, the \defii{Stoneham}{number} $\stoneham{b}{c}$ is defined as $\fundefeq{b,c}{\stoneham{b}c}{\infinitesum{n}{\natmorethan{\power{c}k}1}{\frac{1}{\power{b}nn}}}$ $\stoneham{b}c=\infinitesum{k}1{\frac{1}{\power{b}{\power{c}k}\power{c}k}}$ \end{definition} \end{modnl} %%% Local Variables: %%% mode: latex %%% TeX-master: t %%% End:
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