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Enrique Andrade Gonzalez 2017-12-05 22:34:10 +00:00
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commit c43a36b693
1 changed files with 17 additions and 18 deletions
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35
03/solutions #3/solution #03.tex
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@ -17,14 +17,15 @@
\item Properly typeset the following command and properly refere to it in the text \item Properly typeset the following command and properly refere to it in the text
\begin{align} \begin{align}
(\sum_{i_1,\dots,i_m} a_{i_1,\dots,i_m} ^{2m}{m+1} ^{\frac{m+1}{2m}} \leq C\le \\ (\sum_{i_1,\dots,i_m} a_{i_1,\dots,i_m} ^{2m}(m+1) ^{\frac{m+1}{2m}}) \leq C\le \\
\sup\{ |\sum_{i_1,\dots, i_m} a_{i_1,\dots,i_m} x^1_{i_1}\dots x^m_{i_m}|: \|(x_i^k)_{i=1}^n \|_\infty\leq1,\ 1\leq k\leq m\}, \sup \left\{ \left\|\sum_{i_1,\dots, i_m} a_{i_1,\dots,i_m} x^1_{i_1}\dots x^m_{i_m}\right\|: \|(x_i^k)_{i=1}^n \|_\infty\leq1,\ 1\leq k\leq m\right\},
\end{align} \end{align}
%---------------------------------------------------------------------------------------------- %----------------------------------------------------------------------------------------------
% ¿Es correcto? % ¿Es correcto?
% ¿Is good? % ¿Is good?
\item Properly typset the expression: \[R \in z\] \item Properly typset the expression: \[
\operatorname{Re} z\]
@ -45,20 +46,20 @@ k=2\end{subarray}}^\infty a_n^k
%---------------------------------------------------------------------------------------------- %----------------------------------------------------------------------------------------------
% ¿Es correcto? % ¿Es correcto?
% ¿Is good? % ¿Is good?
\begin{theorem} \begin{theorem}[Cauchy--Hadamard] The radius of convergence $R$ of the power series
(Cauchy--Hadamard) \emph{The radius of convergence $R$ of the power series
\[ \[
\sum_{n=0}^\infty a_n(z-z_0)^n\ \ \ \ \ |z-z_0|<R \sum_{n=0}^\infty a_n(z-z_0)^n\quad |z-z_0|<R
\] \]
can by calculated via the following formula can by calculated via the following formula
\[ \[
\frac{1}{R}=limsup_{n\to\infty} \sqrt[n]{|a_n|}. \frac{1}{R}=\limsup_{n\to\infty} \sqrt[n]{|a_n|}.
\]} \]
\begin{defn}
(Prime numbers) A number is called prime, if it is not compound.
\end{defn}
\end{theorem} \end{theorem}
\begin{defn}[Prime numbers]
A number is called prime, if it is not compound.
\end{defn}
%---------------------------------------------------------------------------------------------- %----------------------------------------------------------------------------------------------
@ -67,15 +68,14 @@ can by calculated via the following formula
\item Typeset the follwing matrix (display-style): \item Typeset the follwing matrix (display-style):
\[ \[
\left\{\begin{array}{cc} \begin{pmatrix}
a_{11} & a_{12}\\ a_{11} & a_{12}\\
a_{21} & a_{22} a_{21} & a_{22}
\end{array} \end{pmatrix}
\right\} \]
\]
and in the text and in the text
$ $
\left(\begin{smallmatrix}{cc} \left(\begin{smallmatrix}
a_{11} & a_{12}\\ a_{11} & a_{12}\\
a_{21} & a_{22} a_{21} & a_{22}
\end{smallmatrix}\right) \end{smallmatrix}\right)
@ -88,5 +88,4 @@ $ Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do
sunt in culpa qui officia deserunt mollit anim id est laborum. sunt in culpa qui officia deserunt mollit anim id est laborum.
\end{enumerate} \end{enumerate}
\end{document} \end{document}