#LyX 2.4 created this file. For more info see https://www.lyx.org/ \lyxformat 572 \begin_document \begin_header \save_transient_properties true \origin unavailable \textclass scrartcl \begin_preamble \usepackage{a4wide} \end_preamble \use_default_options false \maintain_unincluded_children false \language ngerman \language_package default \inputencoding auto \fontencoding auto \font_roman "ae" "default" \font_sans "default" "default" \font_typewriter "default" "default" \font_math "auto" "auto" \font_default_family default \use_non_tex_fonts false \font_sc false \font_osf false \font_sf_scale 100 100 \font_tt_scale 100 100 \use_microtype false \use_dash_ligatures true \graphics default \default_output_format default \output_sync 0 \bibtex_command default \index_command default \float_placement h \paperfontsize 12 \spacing single \use_hyperref false \papersize default \use_geometry false \use_package amsmath 2 \use_package amssymb 2 \use_package cancel 1 \use_package esint 0 \use_package mathdots 0 \use_package mathtools 1 \use_package mhchem 1 \use_package stackrel 1 \use_package stmaryrd 1 \use_package undertilde 1 \cite_engine basic \cite_engine_type default \biblio_style plain \use_bibtopic false \use_indices false \paperorientation portrait \suppress_date false \justification true \use_refstyle 0 \use_minted 0 \index Stichwortverzeichnis \shortcut idx \color #008000 \end_index \secnumdepth 3 \tocdepth 3 \paragraph_separation skip \defskip medskip \is_math_indent 1 \math_indentation default \math_numbering_side default \quotes_style german \dynamic_quotes 0 \papercolumns 1 \papersides 1 \paperpagestyle plain \tablestyle default \tracking_changes false \output_changes false \html_math_output 0 \html_css_as_file 0 \html_be_strict false \end_header \begin_body \begin_layout Standard \begin_inset FormulaMacro \newcommand{\abc}[1][42]{\sin\left(\frac{-3}{#1}\right)} \end_inset \end_layout \begin_layout Standard \begin_inset FormulaMacro \newcommand{\xyz}[2][42][28]{\sqrt{#1}+\ln\left(\frac{#2}{82}\right)} \end_inset \end_layout \begin_layout Standard \begin_inset FormulaMacro \renewcommand{\abc}{asdf} \end_inset \end_layout \begin_layout Standard \begin_inset Formula \begin{align*} \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}]\\ \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] \end{align*} \end_inset \end_layout \begin_layout Standard \begin_inset Formula \begin{align*} \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}]\\ \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] \end{align*} \end_inset \begin_inset Formula \begin{align*} \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}]\\ \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] \end{align*} \end_inset \begin_inset Formula \begin{align*} \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}]\\ \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] \end{align*} \end_inset \begin_inset Formula \begin{align*} \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}]\\ \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] \end{align*} \end_inset \begin_inset Formula \begin{align*} \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}]\\ \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] \end{align*} \end_inset \begin_inset Formula \begin{align*} \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}]\\ \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] \end{align*} \end_inset \begin_inset Formula \begin{align*} \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}]\\ \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] \end{align*} \end_inset \begin_inset Formula \begin{align*} \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}]\\ \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] \end{align*} \end_inset \begin_inset Formula \begin{align*} \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}]\\ \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] \end{align*} \end_inset \begin_inset Formula \begin{align*} \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}]\\ \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] \end{align*} \end_inset \begin_inset Formula \begin{align*} \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}]\\ \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] \end{align*} \end_inset \begin_inset Formula \begin{align*} \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}]\\ \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] \end{align*} \end_inset \begin_inset Formula \begin{align*} \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}]\\ \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] \end{align*} \end_inset \begin_inset Formula \begin{align*} \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}]\\ \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] \end{align*} \end_inset \begin_inset Formula \begin{align*} \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}]\\ \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] \end{align*} \end_inset \begin_inset Formula \begin{align*} \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}]\\ \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] \end{align*} \end_inset \begin_inset Formula \begin{align*} \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}]\\ \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] \end{align*} \end_inset \begin_inset Formula \begin{align*} \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}]\\ \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] \end{align*} \end_inset \begin_inset Formula \begin{align*} \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}]\\ \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] \end{align*} \end_inset \begin_inset Formula \begin{align*} \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}]\\ \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] \end{align*} \end_inset \begin_inset Formula \begin{align*} \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}]\\ \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] \end{align*} \end_inset \begin_inset Formula \begin{align*} \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}]\\ \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] \end{align*} \end_inset \begin_inset Formula \begin{align*} \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}]\\ \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] \end{align*} \end_inset \begin_inset Formula \begin{align*} \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}]\\ \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] \end{align*} \end_inset \begin_inset Formula \begin{align*} \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}]\\ \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] \end{align*} \end_inset \begin_inset Formula \begin{align*} \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}]\\ \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] \end{align*} \end_inset \begin_inset Formula \begin{align*} \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}]\\ \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] \end{align*} \end_inset \begin_inset Formula \begin{align*} \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}]\\ \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] \end{align*} \end_inset \begin_inset Formula \begin{align*} \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}]\\ \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] \end{align*} \end_inset \begin_inset Formula \begin{align*} \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}]\\ \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] \end{align*} \end_inset \begin_inset Formula \begin{align*} \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}]\\ \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] \end{align*} \end_inset \begin_inset Formula \begin{align*} \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}]\\ \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] \end{align*} \end_inset \begin_inset Formula \begin{align*} \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}]\\ \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] \end{align*} \end_inset \begin_inset Formula \begin{align*} \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}]\\ \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] \end{align*} \end_inset \begin_inset Formula \begin{align*} \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}]\\ \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] & \xyz[1][{\xyz[{\xyz[{\xyz[1][2]}][2]}][{\xyz[1][2]}]}] \end{align*} \end_inset \end_layout \end_body \end_document