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Examples from the TeXbook (Chapter 18)

TeXbook p. 162
\sin 2\theta = 2\sin\theta\cos\theta\quad O(n\log n\log\log n)\quad \Pr(X>x)=\exp(-x/\mu)\quad
\max_{1\le n\le m} \log_2 P_n \quad \lim_{x\to 0} {\sin x\over x} = 1

TeXbook p. 163, Exercise 18.2
p_1(n) = \lim_{m\to\infty} \sum_{\nu=0}^\infty \bigl(1-\cos^{2m}(\nu!^n\pi/n)\bigr)

TeXbook p. 163
\sqrt{{\rm Var}(X)} \qquad {\textstyle x_{\rm max} - x_{\rm max}} \qquad {\rm LL}(k) \Rightarrow {\rm LR}(k)
\exp(x+{\rm constant}) \qquad x^3 + \hbox{lower order terms}

\lim_{n\to\infty} x_n {\rm\ exists} \iff \limsup_{n\to\infty} x_n = \liminf_{n\to\infty} x_n

TeXbook p. 164
\gcd(m,n) = \gcd(n,m\bmod n)\qquad x\equiv y+1\pmod{m^2}

{n\choose k} \equiv {\lfloor n/p\rfloor \choose \lfloor k/p\rfloor} {{n\bmod p} \choose {k\bmod p}} \pmod p

{\bf a+b = \Phi_m}\quad {\cal A, B, \ldots, M,N,\ldots, X,Y,Z}

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Created: 14 Mar 2004
Last modified: Mar 15, 2009 1:04:02 PM
Comments to: dpvc@union.edu
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