1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
|
%% plain TeX file
\input antt-math
\seventeenpoint
\font\bigbf=qx-anttm at17pt
\nopagenumbers
\centerline{\bigbf Mathematical Examples Typeset by Antykwa Toru\'nska}
\bigskip
$$\Leftarrow\Longrightarrow\Longleftarrow\longrightarrow\longleftarrow$$
$$
\overleftarrow{Janusz}\overrightarrow{Nowacki}
\longmapsto\bowtie\hookleftarrow\notin\rightleftharpoons
\doteq\langle
$$
$$
\root 2 \of {1+
\root 3 \of {1+
\root 4 \of {1+
\root 5 \of {1+
\root 6 \of {1+
\root 7 \of {1+
\root 8 \of {1+x}}}}}}}
$$
\bigskip
$$\prod_{j<0}\biggl(\sum_{k\ge0}{\mit\Gamma}_{jk}z^k\biggr)
=\sum_{0\ge0}z^n\,\Biggl(\sum_
{\scriptstyle k_0,k_1,\ldots\ge0\atop
\scriptstyle k_0+k_1+\cdots=n}
a_{0k_0}a_{1k_1}\ldots\,\Biggr).$$
\bigskip
\tenpoint
$${(n_1^2<n_2+\cdots+n_m)!\over n_1!\,n_2!\ldots n_m!}
={n_1+n_2\choose n_2}{n_1+n_2+n_3\choose n_3}
\ldots{n_1+n_2+\cdots+n_m\choose n_m}.$$
\bigskip
$$\def\\#1#2{(1-q^{#1_#2+n})} % to save typing
\Pi_R{a_1,a_2,\ldots,a_M\atopwithdelims[]b_1,b_2,\ldots,b_N}
=\prod_{n=0}^R{\\a1\\a2\ldots\\aM\over\\b1\\b2\ldots\\bN}.$$
\bigskip
$$\{\underbrace{\overbrace{\mathstrut {\mit \Psi},\ldots,\Psi}
^{k\;a\mathchar`'\rm s},
\overbrace{\mathstrut {\cal A},\ldots,{\cal B}}
^{l\;b\mathchar`'\rm \acute{s}}}_{k+l\rm\;element}\}.$$
\bigskip
$$\pmatrix{\pmatrix{a&b\cr c&d\cr}&
\pmatrix{e&f\cr g&h\cr}\cr
\noalign{\smallskip}
0&\pmatrix{i&j\cr k&l\cr}\cr}.$$
\bigskip
$$\det\left[\,\matrix{
c_0&c_1\hfill&c_2\hfill&\ldots&c_n\hfill\cr
c_1&c_2\hfill&c_3\hfill&\ldots&c_{n+1}\hfill\cr
c_2&c_3\hfill&c_4\hfill&\ldots&c_{n+2}\hfill\cr
\,\vdots\hfill&\,\vdots\hfill&
\,\vdots\hfill&&\,\vdots\hfill\cr
c_n&c_{n+1}\hfill&c_{n+2}\hfill&\ldots&c_{2n}\hfill\cr
}\right)>0.$$
\bye
|