\documentclass{article}
\usepackage{ifthen}
\usepackage{epsfig}
\usepackage[utf8]{inputenc}
\usepackage{xcolor}
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\usepackage{amsmath}

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  \makeatletter
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  \doxynewunicodechar{²}{${}^{2}$}% Superscript two
  \doxynewunicodechar{³}{${}^{3}$}% Superscript three

\pagestyle{empty}
\begin{document}
\[
    x_{i+1}\leftarrow(ax_{i} + c) \bmod m 
\]
\pagebreak

$1$
\pagebreak

\[
    x_{i}\leftarrow(x_{i - s} - x_{i - r} - carry_{i-1}) \bmod m 
\]
\pagebreak

$r$
\pagebreak

$(m^r - m^s - 1)$
\pagebreak

\[
    p(x|\mu,\sigma) = \frac{1}{\sigma \sqrt{2 \pi}}
           e^{- \frac{{x - \mu}^ {2}}{2 \sigma ^ {2}} } 
\]
\pagebreak

\[
    p(x|m,s) = \frac{1}{sx\sqrt{2\pi}}
               \exp{-\frac{(\ln{x} - m)^2}{2s^2}} 
\]
\pagebreak

\[
    p(x|\alpha,\beta) = \frac{1}{\beta\Gamma(\alpha)}
                        (x/\beta)^{\alpha - 1} e^{-x/\beta} 
\]
\pagebreak

$p(x|n) = \frac{x^{(n/2) - 1}e^{-x/2}}{\Gamma(n/2) 2^{n/2}}$
\pagebreak

$p(x|a,b) = (\pi b (1 + (\frac{x-a}{b})^2))^{-1}$
\pagebreak

\[
    p(x|m,n) = \frac{\Gamma((m+n)/2)}{\Gamma(m/2)\Gamma(n/2)}
               (\frac{m}{n})^{m/2} x^{(m/2)-1}
               (1 + \frac{mx}{n})^{-(m+n)/2} 
\]
\pagebreak

\[
    p(x|n) = \frac{1}{\sqrt(n\pi)} \frac{\Gamma((n+1)/2)}{\Gamma(n/2)}
             (1 + \frac{x^2}{n}) ^{-(n+1)/2} 
\]
\pagebreak

$p$
\pagebreak

$(1 - p)$
\pagebreak

$p(i|t,p) = \binom{t}{i} p^i (1 - p)^{t - i}$
\pagebreak

$t$
\pagebreak

$p(i|p) = p(1 - p)^{i}$
\pagebreak

$p(i) = \binom{n}{i} p^i (1 - p)^{t - i}$
\pagebreak

$p(i|\mu) = \frac{\mu^i}{i!} e^{-\mu}$
\pagebreak

$\mu$
\pagebreak

$p(x|\lambda) = \lambda e^{-\lambda x}$
\pagebreak

$\frac{1}{\lambda}$
\pagebreak

$\frac{\ln 2}{\lambda}$
\pagebreak

$zero$
\pagebreak

$[0, \infty]$
\pagebreak

\[
    p(x|\alpha,\beta) = \frac{\alpha}{\beta} (\frac{x}{\beta})^{\alpha-1}
                        \exp{(-(\frac{x}{\beta})^\alpha)} 
\]
\pagebreak

\[
    p(x|a,b) = \frac{1}{b}
               \exp( \frac{a-x}{b} - \exp(\frac{a-x}{b})) 
\]
\pagebreak

$x_0$
\pagebreak

$ m_{lcg} =
2147483563, a_{lcg} = 40014, c_{lcg} = 0, and lcg(0) = value
$
\pagebreak

$ x_{-r} \dots x_{-1} $
\pagebreak

$ lcg(1) \bmod m
\dots lcg(r) \bmod m $
\pagebreak

$ x_{-1} = 0 $
\pagebreak

$mean$
\pagebreak

$\alpha$
\pagebreak

$\beta$
\pagebreak

$[0, 1]$
\pagebreak

$k$
\pagebreak

$\lambda$
\pagebreak

$a$
\pagebreak

$b$
\pagebreak

\[
  \frac{|f - f_{test}|}{|f_{test}|}
\]
\pagebreak

$ L_n^m(x) $
\pagebreak

$ \alpha $
\pagebreak

$ L_n^\alpha(x) $
\pagebreak

\[
         L_n^\alpha(x) = \frac{(\alpha + 1)_n}{n!}
                         {}_1F_1(-n; \alpha + 1; x)
\]
\pagebreak

$ (\alpha)_n $
\pagebreak

$ {}_1F_1(a; c; x) $
\pagebreak

$ \alpha = m $
\pagebreak

\[
         L_n^m(x) = (-1)^m \frac{d^m}{dx^m} L_{n + m}(x)
\]
\pagebreak

\[
         L_n(x) = \frac{e^x}{n!} \frac{d^n}{dx^n} (x^ne^{-x})
\]
\pagebreak

$ x >= 0 $
\pagebreak

$ P_l(x) $
\pagebreak

\[
  P_l^m(x) = (1 - x^2)^{m/2}\frac{d^m}{dx^m}P_l(x)
\]
\pagebreak

$ B(a,b) $
\pagebreak

$B(a,b)$
\pagebreak

\[
  B(a,b) = \int_0^1 t^{a - 1} (1 - t)^{b - 1} dt
         = \frac{\Gamma(a)\Gamma(b)}{\Gamma(a+b)}
\]
\pagebreak

$ a > 0 $
\pagebreak

$ b > 0 $
\pagebreak

$ E(k) $
\pagebreak

$ K(k) $
\pagebreak

\[
  K(k) = F(k,\pi/2) = \int_0^{\pi/2}\frac{d\theta}
                                             {\sqrt{1 - k^2 sin^2\theta}}
\]
\pagebreak

$ F(k,\phi) $
\pagebreak

$ |k| <= 1 $
\pagebreak

\[
  E(k) = E(k,\pi/2) = \int_0^{\pi/2}\sqrt{1 - k^2 sin^2\theta}
\]
\pagebreak

$ E(k,\phi) $
\pagebreak

$ \Pi(k,\nu) $
\pagebreak

$ \Pi(k,\nu) = \Pi(k,\nu,\pi/2) $
\pagebreak

\[
  \Pi(k,\nu) = \Pi(k,\nu,\pi/2) = \int_0^{\pi/2}
                     \frac{d\theta}
                   {(1 - \nu \sin^2\theta)\sqrt{1 - k^2 \sin^2\theta}}
\]
\pagebreak

$ \Pi(k,\nu,\phi) $
\pagebreak

$ I_{\nu}(x) $
\pagebreak

$ \nu $
\pagebreak

\[
 I_{\nu}(x) = i^{-\nu}J_\nu(ix) = \sum_{k=0}^{\infty}
                \frac{(x/2)^{\nu + 2k}}{k!\Gamma(\nu+k+1)}
\]
\pagebreak

$ J_{\nu}(x) $
\pagebreak

\[
   J_{\nu}(x) = \sum_{k=0}^{\infty}
             \frac{(-1)^k (x/2)^{\nu + 2k}}{k!\Gamma(\nu+k+1)}
\]
\pagebreak

$ K_{\nu}(x) $
\pagebreak

$ x $
\pagebreak

\[
        K_{\nu}(x) = \frac{\pi}{2}
                     \frac{I_{-\nu}(x) - I_{\nu}(x)}{\sin \nu\pi}
\]
\pagebreak

$ \nu = n $
\pagebreak

$ lim_{\nu \to n} $
\pagebreak

\[
        K_{-\nu}(x) = K_{\nu}(x)
\]
\pagebreak

$ N_{\nu}(x) $
\pagebreak

\[
   N_{\nu}(x) = \frac{J_{\nu}(x) \cos \nu\pi - J_{-\nu}(x)}
                     {\sin \nu\pi}
\]
\pagebreak

$ k $
\pagebreak

$ \phi $
\pagebreak

\[
  F(k,\phi) = \int_0^{\phi}\frac{d\theta}
                                     {\sqrt{1 - k^2 sin^2\theta}}
\]
\pagebreak

$ \phi= \pi/2 $
\pagebreak

\[
  E(k,\phi) = \int_0^{\phi} \sqrt{1 - k^2 sin^2\theta}
\]
\pagebreak

\[
  \Pi(k,\nu,\phi) = \int_0^{\phi}
                         \frac{d\theta}
                         {(1 - \nu \sin^2\theta)
                          \sqrt{1 - k^2 \sin^2\theta}}
\]
\pagebreak

$ Ei(x) $
\pagebreak

\[
  Ei(x) = -\int_{-x}^\infty \frac{e^t}{t} dt
\]
\pagebreak

$ H_n(x) $
\pagebreak

\[
  H_n(x) = (-1)^n e^{x^2} \frac{d^n}{dx^n} e^{-x^2}
\]
\pagebreak

\[
  H_n(-x) = (-1)^n H_n(x)
\]
\pagebreak

$ L_n(x) $
\pagebreak

$ l $
\pagebreak

$ |x| <= 0 $
\pagebreak

\[
  P_l(x) = \frac{1}{2^l l!}\frac{d^l}{dx^l}(x^2 - 1)^{l}
\]
\pagebreak

$ l >= 0 $
\pagebreak

$ \zeta(s) $
\pagebreak

$ s $
\pagebreak

\[
        \zeta(s) = \sum_{k=1}^{\infty} k^{-s} \hbox{ for } s > 1
\]
\pagebreak

\[
        \zeta(s) = \frac{1}{1-2^{1-s}}\sum_{k=1}^{\infty}(-1)^{k-1}k^{-s}
             \hbox{ for } 0 <= s <= 1
\]
\pagebreak

\[
        \zeta(s) = 2^s \pi^{s-1} \sin(\frac{\pi s}{2}) \Gamma(1-s) \zeta(1-s)
\]
\pagebreak

$ j_n(x) $
\pagebreak

\[
 j_n(x) = \left(\frac{\pi}{2x} \right) ^{1/2} J_{n+1/2}(x)
\]
\pagebreak

$ \theta $
\pagebreak

\[
 Y_l^m(\theta,\phi) = (-1)^m[\frac{(2l+1)}{4\pi}
                             \frac{(l-m)!}{(l+m)!}]
                  P_l^m(\cos\theta) \exp^{im\phi}
\]
\pagebreak

$ n >= 0 $
\pagebreak

\[
   n_n(x) = \left(\frac{\pi}{2x} \right) ^{1/2} N_{n+1/2}(x)
\]
\pagebreak

$ Ai(x) $
\pagebreak

$ Bi(x) $
\pagebreak

$ {}_1F_1(a;c;x) $
\pagebreak

\[
   {}_1F_1(a;c;x) = \sum_{n=0}^{\infty} \frac{(a)_n x^n}{(c)_n n!}
\]
\pagebreak

$ (x)_k = (x)(x+1)...(x+k-1) $
\pagebreak

$ (x)_0 = 1 $
\pagebreak

$ {}_2F_1(a,b;c;x) $
\pagebreak

\[
   {}_2F_1(a;c;x) = \sum_{n=0}^{\infty} \frac{(a)_n (b)_n x^n}{(c)_n n!}
\]
\pagebreak

$[min, max]$
\pagebreak

$\sqrt{\mathrm{end} - \mathrm{begin}}$
\pagebreak

$1/(\mathrm{oversampling} \cdot \mathrm{num\_parts})$
\pagebreak

\end{document}
