\form#0:\[ x_{i+1}\leftarrow(ax_{i} + c) \bmod m \]
\form#1:$1$
\form#2:\[ x_{i}\leftarrow(x_{i - s} - x_{i - r} - carry_{i-1}) \bmod m \]
\form#3:$r$
\form#4:$(m^r - m^s - 1)$
\form#5:\[ p(x|\mu,\sigma) = \frac{1}{\sigma \sqrt{2 \pi}} e^{- \frac{{x - \mu}^ {2}}{2 \sigma ^ {2}} } \]
\form#6:\[ p(x|m,s) = \frac{1}{sx\sqrt{2\pi}} \exp{-\frac{(\ln{x} - m)^2}{2s^2}} \]
\form#7:\[ p(x|\alpha,\beta) = \frac{1}{\beta\Gamma(\alpha)} (x/\beta)^{\alpha - 1} e^{-x/\beta} \]
\form#8:$p(x|n) = \frac{x^{(n/2) - 1}e^{-x/2}}{\Gamma(n/2) 2^{n/2}}$
\form#9:$p(x|a,b) = (\pi b (1 + (\frac{x-a}{b})^2))^{-1}$
\form#10:\[ p(x|m,n) = \frac{\Gamma((m+n)/2)}{\Gamma(m/2)\Gamma(n/2)} (\frac{m}{n})^{m/2} x^{(m/2)-1} (1 + \frac{mx}{n})^{-(m+n)/2} \]
\form#11:\[ p(x|n) = \frac{1}{\sqrt(n\pi)} \frac{\Gamma((n+1)/2)}{\Gamma(n/2)} (1 + \frac{x^2}{n}) ^{-(n+1)/2} \]
\form#12:$p$
\form#13:$(1 - p)$
\form#14:$p(i|t,p) = \binom{t}{i} p^i (1 - p)^{t - i}$
\form#15:$t$
\form#16:$p(i|p) = p(1 - p)^{i}$
\form#17:$p(i) = \binom{n}{i} p^i (1 - p)^{t - i}$
\form#18:$p(i|\mu) = \frac{\mu^i}{i!} e^{-\mu}$
\form#19:$\mu$
\form#20:$p(x|\lambda) = \lambda e^{-\lambda x}$
\form#21:$\frac{1}{\lambda}$
\form#22:$\frac{\ln 2}{\lambda}$
\form#23:$zero$
\form#24:$[0, \infty]$
\form#25:\[ p(x|\alpha,\beta) = \frac{\alpha}{\beta} (\frac{x}{\beta})^{\alpha-1} \exp{(-(\frac{x}{\beta})^\alpha)} \]
\form#26:\[ p(x|a,b) = \frac{1}{b} \exp( \frac{a-x}{b} - \exp(\frac{a-x}{b})) \]
\form#27:$x_0$
\form#28:$ m_{lcg} = 2147483563, a_{lcg} = 40014, c_{lcg} = 0, and lcg(0) = value $
\form#29:$ x_{-r} \dots x_{-1} $
\form#30:$ lcg(1) \bmod m \dots lcg(r) \bmod m $
\form#31:$ x_{-1} = 0 $
\form#32:$mean$
\form#33:$\alpha$
\form#34:$\beta$
\form#35:$[0, 1]$
\form#36:$k$
\form#37:$\lambda$
\form#38:$a$
\form#39:$b$
\form#40:\[ \frac{|f - f_{test}|}{|f_{test}|} \]
\form#41:$ L_n^m(x) $
\form#42:$ \alpha $
\form#43:$ L_n^\alpha(x) $
\form#44:\[ L_n^\alpha(x) = \frac{(\alpha + 1)_n}{n!} {}_1F_1(-n; \alpha + 1; x) \]
\form#45:$ (\alpha)_n $
\form#46:$ {}_1F_1(a; c; x) $
\form#47:$ \alpha = m $
\form#48:\[ L_n^m(x) = (-1)^m \frac{d^m}{dx^m} L_{n + m}(x) \]
\form#49:\[ L_n(x) = \frac{e^x}{n!} \frac{d^n}{dx^n} (x^ne^{-x}) \]
\form#50:$ x >= 0 $
\form#51:$ P_l(x) $
\form#52:\[ P_l^m(x) = (1 - x^2)^{m/2}\frac{d^m}{dx^m}P_l(x) \]
\form#53:$ B(a,b) $
\form#54:$B(a,b)$
\form#55:\[ B(a,b) = \int_0^1 t^{a - 1} (1 - t)^{b - 1} dt = \frac{\Gamma(a)\Gamma(b)}{\Gamma(a+b)} \]
\form#56:$ a > 0 $
\form#57:$ b > 0 $
\form#58:$ E(k) $
\form#59:$ K(k) $
\form#60:\[ K(k) = F(k,\pi/2) = \int_0^{\pi/2}\frac{d\theta} {\sqrt{1 - k^2 sin^2\theta}} \]
\form#61:$ F(k,\phi) $
\form#62:$ |k| <= 1 $
\form#63:\[ E(k) = E(k,\pi/2) = \int_0^{\pi/2}\sqrt{1 - k^2 sin^2\theta} \]
\form#64:$ E(k,\phi) $
\form#65:$ \Pi(k,\nu) $
\form#66:$ \Pi(k,\nu) = \Pi(k,\nu,\pi/2) $
\form#67:\[ \Pi(k,\nu) = \Pi(k,\nu,\pi/2) = \int_0^{\pi/2} \frac{d\theta} {(1 - \nu \sin^2\theta)\sqrt{1 - k^2 \sin^2\theta}} \]
\form#68:$ \Pi(k,\nu,\phi) $
\form#69:$ I_{\nu}(x) $
\form#70:$ \nu $
\form#71:\[ I_{\nu}(x) = i^{-\nu}J_\nu(ix) = \sum_{k=0}^{\infty} \frac{(x/2)^{\nu + 2k}}{k!\Gamma(\nu+k+1)} \]
\form#72:$ J_{\nu}(x) $
\form#73:\[ J_{\nu}(x) = \sum_{k=0}^{\infty} \frac{(-1)^k (x/2)^{\nu + 2k}}{k!\Gamma(\nu+k+1)} \]
\form#74:$ K_{\nu}(x) $
\form#75:$ x $
\form#76:\[ K_{\nu}(x) = \frac{\pi}{2} \frac{I_{-\nu}(x) - I_{\nu}(x)}{\sin \nu\pi} \]
\form#77:$ \nu = n $
\form#78:$ lim_{\nu \to n} $
\form#79:\[ K_{-\nu}(x) = K_{\nu}(x) \]
\form#80:$ N_{\nu}(x) $
\form#81:\[ N_{\nu}(x) = \frac{J_{\nu}(x) \cos \nu\pi - J_{-\nu}(x)} {\sin \nu\pi} \]
\form#82:$ k $
\form#83:$ \phi $
\form#84:\[ F(k,\phi) = \int_0^{\phi}\frac{d\theta} {\sqrt{1 - k^2 sin^2\theta}} \]
\form#85:$ \phi= \pi/2 $
\form#86:\[ E(k,\phi) = \int_0^{\phi} \sqrt{1 - k^2 sin^2\theta} \]
\form#87:\[ \Pi(k,\nu,\phi) = \int_0^{\phi} \frac{d\theta} {(1 - \nu \sin^2\theta) \sqrt{1 - k^2 \sin^2\theta}} \]
\form#88:$ Ei(x) $
\form#89:\[ Ei(x) = -\int_{-x}^\infty \frac{e^t}{t} dt \]
\form#90:$ H_n(x) $
\form#91:\[ H_n(x) = (-1)^n e^{x^2} \frac{d^n}{dx^n} e^{-x^2} \]
\form#92:\[ H_n(-x) = (-1)^n H_n(x) \]
\form#93:$ L_n(x) $
\form#94:$ l $
\form#95:$ |x| <= 0 $
\form#96:\[ P_l(x) = \frac{1}{2^l l!}\frac{d^l}{dx^l}(x^2 - 1)^{l} \]
\form#97:$ l >= 0 $
\form#98:$ \zeta(s) $
\form#99:$ s $
\form#100:\[ \zeta(s) = \sum_{k=1}^{\infty} k^{-s} \hbox{ for } s > 1 \]
\form#101:\[ \zeta(s) = \frac{1}{1-2^{1-s}}\sum_{k=1}^{\infty}(-1)^{k-1}k^{-s} \hbox{ for } 0 <= s <= 1 \]
\form#102:\[ \zeta(s) = 2^s \pi^{s-1} \sin(\frac{\pi s}{2}) \Gamma(1-s) \zeta(1-s) \]
\form#103:$ j_n(x) $
\form#104:\[ j_n(x) = \left(\frac{\pi}{2x} \right) ^{1/2} J_{n+1/2}(x) \]
\form#105:$ \theta $
\form#106:\[ Y_l^m(\theta,\phi) = (-1)^m[\frac{(2l+1)}{4\pi} \frac{(l-m)!}{(l+m)!}] P_l^m(\cos\theta) \exp^{im\phi} \]
\form#107:$ n >= 0 $
\form#108:\[ n_n(x) = \left(\frac{\pi}{2x} \right) ^{1/2} N_{n+1/2}(x) \]
\form#109:$ Ai(x) $
\form#110:$ Bi(x) $
\form#111:$ {}_1F_1(a;c;x) $
\form#112:\[ {}_1F_1(a;c;x) = \sum_{n=0}^{\infty} \frac{(a)_n x^n}{(c)_n n!} \]
\form#113:$ (x)_k = (x)(x+1)...(x+k-1) $
\form#114:$ (x)_0 = 1 $
\form#115:$ {}_2F_1(a,b;c;x) $
\form#116:\[ {}_2F_1(a;c;x) = \sum_{n=0}^{\infty} \frac{(a)_n (b)_n x^n}{(c)_n n!} \]
\form#117:$[min, max]$
\form#118:$\sqrt{\mathrm{end} - \mathrm{begin}}$
\form#119:$1/(\mathrm{oversampling} \cdot \mathrm{num\_parts})$