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1 #LyX 1.5.2 created this file. For more info see http://www.lyx.org/
2 \lyxformat 295
3 \begin_document
4 \begin_header
5 \textclass scrartcl
6 \begin_preamble
7 \usepackage{a4wide}
8 \end_preamble
9 \options fleqn
10 \language ngerman
11 \inputencoding auto
12 \font_roman ae
13 \font_sans default
14 \font_typewriter default
15 \font_default_family default
16 \font_sc false
17 \font_osf false
18 \font_sf_scale 100
19 \font_tt_scale 100
20 \graphics default
21 \float_placement h
22 \paperfontsize 12
23 \spacing single
24 \use_hyperref false
25 \papersize default
26 \use_geometry false
27 \use_amsmath 2
28 \use_esint 0
29 \cite_engine basic
30 \use_bibtopic false
31 \paperorientation portrait
32 \secnumdepth 3
33 \tocdepth 3
34 \paragraph_separation skip
35 \defskip medskip
36 \quotes_language german
37 \papercolumns 1
38 \papersides 1
39 \paperpagestyle plain
40 \tracking_changes false
41 \output_changes false
42 \author "" 
43 \author "" 
44 \end_header
45
46 \begin_body
47
48 \begin_layout Standard
49 \begin_inset FormulaMacro
50 \newcommand{\abc}[1][42]{\sin\left(\frac{-3}{#1}\right)}
51 \end_inset
52
53
54 \end_layout
55
56 \begin_layout Standard
57 \begin_inset FormulaMacro
58 \newcommand{\xyz}[2][42][28]{\sqrt{#1}+\ln\left(\frac{#2}{82}\right)}
59 \end_inset
60
61
62 \end_layout
63
64 \begin_layout Standard
65 \begin_inset FormulaMacro
66 \renewcommand{\abc}{asdf}
67 \end_inset
68
69
70 \end_layout
71
72 \begin_layout Standard
73 \begin_inset Formula \begin{align*}
74 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
75 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
76
77 \end_inset
78
79
80 \end_layout
81
82 \begin_layout Standard
83 \begin_inset Formula \begin{align*}
84 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
85 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
86
87 \end_inset
88
89
90 \begin_inset Formula \begin{align*}
91 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
92 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
93
94 \end_inset
95
96
97 \begin_inset Formula \begin{align*}
98 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
99 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
100
101 \end_inset
102
103
104 \begin_inset Formula \begin{align*}
105 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
106 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
107
108 \end_inset
109
110
111 \begin_inset Formula \begin{align*}
112 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
113 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
114
115 \end_inset
116
117
118 \begin_inset Formula \begin{align*}
119 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
120 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
121
122 \end_inset
123
124
125 \begin_inset Formula \begin{align*}
126 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
127 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
128
129 \end_inset
130
131
132 \begin_inset Formula \begin{align*}
133 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
134 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
135
136 \end_inset
137
138
139 \begin_inset Formula \begin{align*}
140 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
141 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
142
143 \end_inset
144
145
146 \begin_inset Formula \begin{align*}
147 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
148 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
149
150 \end_inset
151
152
153 \begin_inset Formula \begin{align*}
154 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
155 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
156
157 \end_inset
158
159
160 \begin_inset Formula \begin{align*}
161 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
162 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
163
164 \end_inset
165
166
167 \begin_inset Formula \begin{align*}
168 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
169 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
170
171 \end_inset
172
173
174 \begin_inset Formula \begin{align*}
175 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
176 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
177
178 \end_inset
179
180
181 \begin_inset Formula \begin{align*}
182 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
183 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
184
185 \end_inset
186
187
188 \begin_inset Formula \begin{align*}
189 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
190 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
191
192 \end_inset
193
194
195 \begin_inset Formula \begin{align*}
196 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
197 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
198
199 \end_inset
200
201
202 \begin_inset Formula \begin{align*}
203 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
204 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
205
206 \end_inset
207
208
209 \begin_inset Formula \begin{align*}
210 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
211 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
212
213 \end_inset
214
215
216 \begin_inset Formula \begin{align*}
217 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
218 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
219
220 \end_inset
221
222
223 \begin_inset Formula \begin{align*}
224 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
225 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
226
227 \end_inset
228
229
230 \begin_inset Formula \begin{align*}
231 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
232 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
233
234 \end_inset
235
236
237 \begin_inset Formula \begin{align*}
238 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
239 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
240
241 \end_inset
242
243
244 \begin_inset Formula \begin{align*}
245 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
246 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
247
248 \end_inset
249
250
251 \begin_inset Formula \begin{align*}
252 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
253 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
254
255 \end_inset
256
257
258 \begin_inset Formula \begin{align*}
259 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
260 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
261
262 \end_inset
263
264
265 \begin_inset Formula \begin{align*}
266 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
267 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
268
269 \end_inset
270
271
272 \begin_inset Formula \begin{align*}
273 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
274 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
275
276 \end_inset
277
278
279 \begin_inset Formula \begin{align*}
280 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
281 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
282
283 \end_inset
284
285
286 \begin_inset Formula \begin{align*}
287 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
288 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
289
290 \end_inset
291
292
293 \begin_inset Formula \begin{align*}
294 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
295 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
296
297 \end_inset
298
299
300 \begin_inset Formula \begin{align*}
301 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
302 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
303
304 \end_inset
305
306
307 \begin_inset Formula \begin{align*}
308 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
309 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
310
311 \end_inset
312
313
314 \begin_inset Formula \begin{align*}
315 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
316 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
317
318 \end_inset
319
320
321 \begin_inset Formula \begin{align*}
322 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
323 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
324
325 \end_inset
326
327
328 \end_layout
329
330 \end_body
331 \end_document