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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
47 \begin_body
48
49 \begin_layout Standard
50 \begin_inset FormulaMacro
51 \newcommand{\abc}[1][42]{\sin\left(\frac{-3}{#1}\right)}
52 \end_inset
53
54
55 \end_layout
56
57 \begin_layout Standard
58 \begin_inset FormulaMacro
59 \newcommand{\xyz}[2][42][28]{\sqrt{#1}+\ln\left(\frac{#2}{82}\right)}
60 \end_inset
61
62
63 \end_layout
64
65 \begin_layout Standard
66 \begin_inset FormulaMacro
67 \renewcommand{\abc}{asdf}
68 \end_inset
69
70
71 \end_layout
72
73 \begin_layout Standard
74 \begin_inset Formula \begin{align*}
75 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
76 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
77
78 \end_inset
79
80
81 \end_layout
82
83 \begin_layout Standard
84 \begin_inset Formula \begin{align*}
85 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
86 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
87
88 \end_inset
89
90
91 \begin_inset Formula \begin{align*}
92 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
93 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
94
95 \end_inset
96
97
98 \begin_inset Formula \begin{align*}
99 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
100 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
101
102 \end_inset
103
104
105 \begin_inset Formula \begin{align*}
106 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
107 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
108
109 \end_inset
110
111
112 \begin_inset Formula \begin{align*}
113 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
114 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
115
116 \end_inset
117
118
119 \begin_inset Formula \begin{align*}
120 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
121 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
122
123 \end_inset
124
125
126 \begin_inset Formula \begin{align*}
127 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
128 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
129
130 \end_inset
131
132
133 \begin_inset Formula \begin{align*}
134 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
135 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
136
137 \end_inset
138
139
140 \begin_inset Formula \begin{align*}
141 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
142 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
143
144 \end_inset
145
146
147 \begin_inset Formula \begin{align*}
148 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
149 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
150
151 \end_inset
152
153
154 \begin_inset Formula \begin{align*}
155 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
156 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
157
158 \end_inset
159
160
161 \begin_inset Formula \begin{align*}
162 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
163 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
164
165 \end_inset
166
167
168 \begin_inset Formula \begin{align*}
169 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
170 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
171
172 \end_inset
173
174
175 \begin_inset Formula \begin{align*}
176 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
177 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
178
179 \end_inset
180
181
182 \begin_inset Formula \begin{align*}
183 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
184 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
185
186 \end_inset
187
188
189 \begin_inset Formula \begin{align*}
190 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
191 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
192
193 \end_inset
194
195
196 \begin_inset Formula \begin{align*}
197 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
198 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
199
200 \end_inset
201
202
203 \begin_inset Formula \begin{align*}
204 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
205 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
206
207 \end_inset
208
209
210 \begin_inset Formula \begin{align*}
211 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
212 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
213
214 \end_inset
215
216
217 \begin_inset Formula \begin{align*}
218 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
219 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
220
221 \end_inset
222
223
224 \begin_inset Formula \begin{align*}
225 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
226 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
227
228 \end_inset
229
230
231 \begin_inset Formula \begin{align*}
232 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
233 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
234
235 \end_inset
236
237
238 \begin_inset Formula \begin{align*}
239 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
240 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
241
242 \end_inset
243
244
245 \begin_inset Formula \begin{align*}
246 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
247 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
248
249 \end_inset
250
251
252 \begin_inset Formula \begin{align*}
253 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
254 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
255
256 \end_inset
257
258
259 \begin_inset Formula \begin{align*}
260 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
261 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
262
263 \end_inset
264
265
266 \begin_inset Formula \begin{align*}
267 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
268 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
269
270 \end_inset
271
272
273 \begin_inset Formula \begin{align*}
274 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
275 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
276
277 \end_inset
278
279
280 \begin_inset Formula \begin{align*}
281 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
282 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
283
284 \end_inset
285
286
287 \begin_inset Formula \begin{align*}
288 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
289 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
290
291 \end_inset
292
293
294 \begin_inset Formula \begin{align*}
295 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
296 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
297
298 \end_inset
299
300
301 \begin_inset Formula \begin{align*}
302 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
303 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
304
305 \end_inset
306
307
308 \begin_inset Formula \begin{align*}
309 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
310 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
311
312 \end_inset
313
314
315 \begin_inset Formula \begin{align*}
316 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
317 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
318
319 \end_inset
320
321
322 \begin_inset Formula \begin{align*}
323 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
324 \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
325
326 \end_inset
327
328
329 \end_layout
330
331 \end_body
332 \end_document