Commit f633c51e authored by Michael Kohlhase's avatar 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}
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\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}
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\begin{modsig}[creators=miko]{function-zero}
\gimport[smglom/sets]{image}
\gimport[smglom/algebra]{field}
\symi{zero}
\end{modsig}
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\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}
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