jsMath (Examples)

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# Examples from the TeXbook (Chapter 18, Final Exercises)

TeXbook, Exercise 18.28
{\bf S^{\rm-1}TS=dg}(\omega_1,\ldots,\omega_n)=\bf\Lambda

TeXbook, Exercise 18.29
\Pr(\,m=n\mid m+n=3\,)

TeXbook, Exercise 18.30
\sin18^\circ = {1\over 4}(\sqrt5-1)

TeXbook, Exercise 18.31
k=1.38\times 10^{-16}\rm\,erg/^\circ K

TeXbook, Exercise 18.32
\bar\Phi\subset NL_1^*/N=\bar L_1^* \subseteq\cdots\subseteq NL_n^*/N=\bar L_n^*

TeXbook, Exercise 18.33
\textstyle I(\lambda) = \int\!\!\int_Dg(x,y)e^{i\lambda h(x,y)}\,dx\,dy

TeXbook, Exercise 18.34
\textstyle \int_0^1\cdots\int_0^1 f(x_1,\ldots,c_n)\,dx_1\ldots\,dx_n

TeXbook, Exercise 18.35
x_{2m}\equiv\cases{Q(X_m^2-P_2W_m^2)-2S^2&\text{($m$ odd)}\cr \rule 0pt 1.2em 0pt P_2^2(X_m^2-P_2W_m^2)-2S^2&\text{($m$ even)}} \pmod N

TeXbook, Exercise 18.36
(1+x_1z+x_1^2z^2+\cdots\,) \ldots (1+x_nz+x_n^2z^2+\cdots\,) = {1\over(1-x_1z)\ldots(1-x_nz)}

TeXbook, Exercise 18.37
\prod_{j\ge0}\biggl(\sum_{k\ge0}a_{jk}z^k\biggr) = \sum_{n\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)

TeXbook, Exercise 18.38
{(n_1+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}

TeXbook, Exercise 18.39
\Pi_R{a_1,a_2,\ldots,a_M\atopwithdelims[] b_1,b_2,\ldots,b_N} = \prod_{n=0}^R {(1-q^{a_1+n})(1-q^{a_2+n})\ldots(1-q^{a_M+n}) \over (1-q^{b_1+n})(1-q^{b_2+n})\ldots(1-q^{b_N+n})}

TeXbook, Exercise 18.40
\sum_{p\rm\;prime} f(p) = \int_{t > 1} f(t)\,d\pi(t)

TeXbook, Exercise 18.41
\{\underbrace{\overbrace{\mathstrut a,\ldots,a}^{k\;a'\rm s}, \overbrace{\mathstrut b,\ldots,b}^{l\;b'\rm s}\>}_{k+1\rm\;elements}\}

TeXbook, Exercise 18.42
\pmatrix{\pmatrix{a&b\cr c&d} & \pmatrix{e&f\cr g&h}\cr \rule 0pt 2.25em 0pt 0&\pmatrix{i&j\cr k&l}}

TeXbook, Exercise 18.43
\det\left|\,\matrix{ c_0 & c_1 & c_2 & \ldots & c_{n\phantom{+1}}\cr c_1 & c_2 & c_3 & \ldots & c_{n+1}\cr c_2 & c_3 & c_4 & \ldots & c_{n+2}\cr \vdots & \vdots & \vdots & \ddots & \vdots \cr c_n & c_{n+1} & c_{n+2} & \ldots & c_{2n}} \right| > 0

TeXbook, Exercise 18.44
\mathop{{\sum}'}_{x\in A}f(x)\mathrel{\mathop=\limits^{\rm def}} \sum_{\scriptstyle x\in A\atop\scriptstyle x\ne0}f(x)

TeXbook, Exercise 18.45
\textstyle 2\uparrow\uparrow k \mathrel{\mathop=\limits^{\rm def}} 2^{2^{2^{\cdot^{\cdot^{\cdot^2}}}}}\ulap{\Big\}\scriptstyle k}

 jsMath web pages Created: 14 Mar 2004 Last modified: Mar 15, 2009 1:05:01 PM Comments to: dpvc@union.edu