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}