\documentclass{article}
\usepackage{iftex}
\usepackage{ifthen}
\usepackage{epsfig}
\usepackage[utf8]{inputenc}
\usepackage{xcolor}
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  \doxynewunicodechar{²}{${}^{2}$}% Superscript two
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\fi
\pagestyle{empty}
\begin{document}
$f(x_1,\ldots,x_n)$
\pagebreak

$g(x_1,\ldots,x_n)$
\pagebreak

$x_i$
\pagebreak

\[ A(t) = \frac{F(t) - \alpha B(t)}{F(t) + \alpha B(t)} \]
\pagebreak

\[ \Delta f_i^{\rm c} = \pm\sqrt{(\Delta f_i)^2 + (\Delta \mathrm{bkg})^2} = \pm\sqrt{f_i + \mathrm{bkg}} \]
\pagebreak

$ f_i^{\rm c} $
\pagebreak

$ f_i $
\pagebreak

$ \mathrm{bkg} $
\pagebreak

\[ \mathrm{bkg} = \frac{1}{N}\sum_{i=0}^N f_i \]
\pagebreak

\[ \Delta f_i^{\rm c} = \pm\sqrt{(\Delta f_i)^2 + (\Delta \mathrm{bkg})^2} = \pm\sqrt{f_i + (\Delta \mathrm{bkg})^2} \]
\pagebreak

$ N $
\pagebreak

\[ \Delta \mathrm{bkg} = \pm\frac{1}{N}\sqrt{\sum_{i=0}^N f_i} \]
\pagebreak

\[ A_{\rm RRF}(t) = A(t) \cdot 2\cos(\omega_{\rm RRF} t + \phi_{\rm RRF}) \]
\pagebreak

$ A(t) $
\pagebreak

$ A(t) = \frac{F(t) - \alpha B(t)}{F(t) + \alpha B(t)} $
\pagebreak

$ \omega_{\rm RRF} $
\pagebreak

$ \phi_{\rm RRF} $
\pagebreak

\[ \chi^2 = \sum_{i=1}^{N} \frac{(y_i^{\rm data} - y_i^{\rm theory})^2}{\sigma_i^2} \]
\pagebreak

\[ -2\ln L = 2\sum_{i=1}^{N} \left[y_i^{\rm theory} - y_i^{\rm data} \ln(y_i^{\rm theory})\right] \]
\pagebreak

\[ w[n] = \frac{I_0\left(\beta\sqrt{1-\left(\frac{n-\alpha}{\alpha}\right)^2}\right)}{I_0(\beta)} \]
\pagebreak

$ I_0 $
\pagebreak

$ \alpha = (M-1)/2 $
\pagebreak

$ \beta $
\pagebreak

\[ y_{\rm filtered}[n] = \sum_{k=0}^{M-1} h[k] \cdot y_{\rm theory}[n-k] \]
\pagebreak

\[ -2\ln L_{\rm total} = \sum_{i=1}^{N_{\rm runs}} (-2\ln L_i) \]
\pagebreak

\[ -2\ln L = 2\sum_{j=1}^{N_{\rm bins}} \left[y_j^{\rm theory} - y_j^{\rm data} \ln(y_j^{\rm theory})\right] \]
\pagebreak

\[ N_{\rm bins,total} = \sum_{i=1}^{N_{\rm runs}} N_{\rm bins,i} \]
\pagebreak

\[ \chi^2_{\rm red} = \frac{\chi^2}{N_{\rm bins,total} - N_{\rm params}} \]
\pagebreak

\[ \frac{1}{\tau_{\rm eff}} = \frac{1}{\tau_{\mu}} + \lambda_{\rm capture} \]
\pagebreak

\[ \chi^2 = \sum_{i={\rm start}}^{\rm end} \frac{(N_i^{\rm data} - N_i^{\rm theory})^2}{\sigma_i^2} \]
\pagebreak

\[ \chi^2_{\rm expected} = \sum_{i} \frac{(N_i^{\rm data} - N_i^{\rm theory})^2}{N_i^{\rm theory}} \]
\pagebreak

\[ -2\ln L = 2\sum_{i} \left[N_i^{\rm theory} - N_i^{\rm data} \ln(N_i^{\rm theory})\right] \]
\pagebreak

\[ \chi^2 = \sum_{i={\rm start}}^{\rm end} \frac{(y_i^{\rm data} - y_i^{\rm theory})^2}{\sigma_i^2} \]
\pagebreak

\[ N(t) = N_0 e^{-t/\tau_\mu} P(t) + B \]
\pagebreak

\[ \chi^2 = \sum_{i} \frac{(N_i^{\rm data} - N_i^{\rm theory})^2}{\sigma_i^2} \]
\pagebreak

\[P_{\rm RRF}(t) = 2 \cdot P(t) \cdot \cos(\omega_{\rm RRF} t + \phi_{\rm RRF})
\]
\pagebreak

\[P_{\rm RRF}(t) = A \cdot [\cos((\omega - \omega_{\rm RRF})t + \phi - \phi_{\rm RRF}) + \text{high freq.}] \cdot e^{-\lambda t}
\]
\pagebreak

\[\sigma_{A}(t) = \frac{e^{t/\tau_\mu}}{N_0} \sqrt{N(t) + \left(\frac{N(t)-B}{N_0}\right)^2 \sigma_{N_0}^2}
\]
\pagebreak

\[\sigma_{A_{\rm RRF}}^{\rm packed} = \frac{\sqrt{2}}{n} \sqrt{\sum_{i=1}^{n} \sigma_{A}^2(t_i)}
\]
\pagebreak

\[\chi^2 = \sum_{i=t_{\rm start}}^{t_{\rm end}} \frac{[A_{\rm RRF}^{\rm data}(t_i) - A_{\rm RRF}^{\rm theory}(t_i)]^2}{\sigma_i^2}
\]
\pagebreak

\[\chi^2_{\rm exp} = \sum_{i} \frac{[A_{\rm RRF}^{\rm data}(t_i) - A_{\rm RRF}^{\rm theory}(t_i)]^2}{A_{\rm RRF}^{\rm theory}(t_i)}
\]
\pagebreak

\[N_0 = \frac{\sum_{i=0}^{n} M(t_i)}{n}
\]
\pagebreak

\[\sigma_{N_0} = \frac{\sqrt{\sum w_i^2 \sigma_{M_i}^2}}{\sum w_i}
\]
\pagebreak

\[ P(t) = a_0 + a_1 t + a_2 t^2 + a_3 t^3 \]
\pagebreak

$a_0, a_1, a_2, a_3$
\pagebreak

\[ P(t) = \texttt{param[0]} + \texttt{param[1]} \cdot t
         + \texttt{param[2]} \cdot t^2 + \texttt{param[3]} \cdot t^3 \]
\pagebreak

$a_0$
\pagebreak

$a_1$
\pagebreak

$a_2$
\pagebreak

$a_3$
\pagebreak

\[ \Delta A = \pm\frac{2}{(F+B)^2}\sqrt{B^2(\Delta F)^2 + F^2(\Delta B)^2} \]
\pagebreak

$\Delta\mathrm{bkg} = \sqrt{\mathrm{bkg}}$
\pagebreak

\[ \Delta f_i^{\rm c} = \pm\left[ (\Delta f_i)^2 + (\Delta \mathrm{bkg})^2 \right]^{1/2} =
     \pm\left[ f_i + \mathrm{bkg} \right]^{1/2}, \]
\pagebreak

$ f_i^{\rm c} = f_i - \mathrm{bkg} $
\pagebreak

\[ \Delta f_i^{\rm c} = \pm \sqrt{ (\Delta f_i)^2 + (\Delta \mathrm{bkg})^2 } =
   \pm \sqrt{f_i + (\Delta \mathrm{bkg})^2} \]
\pagebreak

$ \Delta \mathrm{bkg} $
\pagebreak

\[ \Delta \mathrm{bkg} = \pm\frac{1}{N}\left[\sum_{i=0}^N (\Delta f_i)^2\right]^{1/2} =
\pm\frac{1}{N}\left[\sum_{i=0}^N f_i \right]^{1/2},\]
\pagebreak

$N$
\pagebreak

$ A_i = (f_i^c-b_i^c)/(f_i^c+b_i^c) $
\pagebreak

$ \delta A_i = 2 \sqrt{(b_i^c)^2 (\delta f_i^c)^2 + (\delta b_i^c)^2 (f_i^c)^2}/(f_i^c+b_i^c)^2$
\pagebreak

$ A_i = (\alpha f_i^c-b_i^c)/(\alpha \beta f_i^c+b_i^c) $
\pagebreak

\[ A_i = \frac{f_i^{\rm c} - b_i^{\rm c}}{f_i^{\rm c} + b_i^{\rm c}} \]
\pagebreak

\[ \Delta A_i = \pm\frac{2}{(f_i^{\rm c}+b_i^{\rm c})^2}\sqrt{
    (b_i^{\rm c})^2 (\Delta f_i^{\rm c})^2 +
    (f_i^{\rm c})^2 (\Delta b_i^{\rm c})^2} \]
\pagebreak

$ b_i^{\rm c} $
\pagebreak

$ A_i = (f_i^{\rm c}-b_i^{\rm c})/(f_i^{\rm c}+b_i^{\rm c}) $
\pagebreak

$ \delta A_i = \frac{2}{(f_i^{\rm c}+b_i^{\rm c})^2}\sqrt{(b_i^{\rm c})^2 (\delta f_i^{\rm c})^2 + (f_i^{\rm c})^2 (\delta b_i^{\rm c})^2} $
\pagebreak

$ \sigma_{\rm packed} = \sqrt{\sum \sigma_i^2}/N_{\rm pack} $
\pagebreak

$ A_i = (\alpha f_i^{\rm c} - b_i^{\rm c})/(\alpha \beta f_i^{\rm c} + b_i^{\rm c}) $
\pagebreak

$ A_R(t) = A(t) \cdot 2\cos(\omega_R t + \phi_R) $
\pagebreak

$ T(t) $
\pagebreak

$ T_R(t) = T(t) \cdot 2\cos(\omega_R t + \phi_R) $
\pagebreak

$ \omega_R $
\pagebreak

$ \phi_R $
\pagebreak

$ A_{\rm RRF}(t) = A(t) \cdot 2\cos(\omega_{\rm RRF} t + \phi_{\rm RRF}) $
\pagebreak

\[ \delta A_i = \frac{2}{(f_i^{\rm c}+b_i^{\rm c})^2}\sqrt{(b_i^{\rm c})^2 (\delta f_i^{\rm c})^2 + (f_i^{\rm c})^2 (\delta b_i^{\rm c})^2} \]
\pagebreak

$ w[n] = \frac{I_0(\beta\sqrt{1-(n/\alpha)^2})}{I_0(\beta)} $
\pagebreak

$ h[n] = \frac{\sin(\omega_c n)}{\pi n} \cdot w[n] $
\pagebreak

\[ y_{\rm filtered}[i] = \sum_{j=0}^{M-1} h[j] \cdot y_{\rm theory}[i-j] \]
\pagebreak

\[ \chi^2_{\rm total} = \sum_{i=1}^{N_{\rm runs}} \chi^2_i \]
\pagebreak

\[ \chi^2_i = \sum_{j=1}^{N_{\rm bins,i}} \frac{(y_j^{\rm data} - y_j^{\rm theory})^2}{\sigma_j^2} \]
\pagebreak

\[ A_i = \frac{F_i - \alpha B_i}{F_i + \alpha B_i} \]
\pagebreak

\[ -2\ln L = 2\sum_{i} \left[N_i^{\rm theory} - N_i^{\rm data}\ln(N_i^{\rm theory})\right] \]
\pagebreak

\[ P(n|\\lambda) = \frac{\\lambda^n e^{-\\lambda}}{n!} \]
\pagebreak

\[ \chi^2 = \sum_{i={\rm start}}^{\rm end} \frac{(y_i - f(x_i))^2}{\sigma_i^2} \]
\pagebreak

\[\chi^2 = \sum_{i=t_{\rm start}}^{t_{\rm end}} \frac{[N_i - N_{\rm theo}(t_i)]^2}{\sigma_i^2}
\]
\pagebreak

\[N_{\rm theo}(t) = N_0 e^{-t/\tau_\mu} [1 + P(t)] + B
\]
\pagebreak

\[\text{correction} = \text{packing} \times (t_{\rm res} \times 1000)
\]
\pagebreak

\[\chi^2_{\rm exp} = \sum_{i=t_{\rm start}}^{t_{\rm end}} \frac{[N_i - N_{\rm theo}(t_i)]^2}{N_{\rm theo}(t_i)}
\]
\pagebreak

\[-2\ln\mathcal{L} = 2 \sum_{i} \left[ N_{\rm theo}(t_i) - N_i + N_i \ln\frac{N_i}{N_{\rm theo}(t_i)} \right]
\]
\pagebreak

\[P(N_i | N_{\rm theo}) = \frac{N_{\rm theo}^{N_i} e^{-N_{\rm theo}}}{N_i!}
\]
\pagebreak

\[-2\ln\mathcal{L}_{\rm exp} = 2 \sum_{i} N_i \ln\frac{N_i}{N_{\rm theo}(t_i)}
\]
\pagebreak

\[N(t) = N_0 e^{-t/\tau_\mu} [1 + P(t)] + B
\]
\pagebreak

$ \lceil \frac{t_{\rm start} - t_{\rm data,0}}{\Delta t} \rceil $
\pagebreak

$ \lfloor \frac{t_{\rm end} - t_{\rm data,0}}{\Delta t} \rfloor + 1 $
\pagebreak

\[ N(t) = N_0 e^{-t/\tau} [ 1 + A(t) ] + \mathrm{Bkg} \]
\pagebreak

\[ A(t) = (-1) + e^{+t/\tau}\, \frac{N(t)-\mathrm{Bkg}}{N_0}. \]
\pagebreak

$ N(t) $
\pagebreak

\[ \Delta A(t) = \frac{e^{t/\tau}}{N_0}\,\sqrt{\frac{N(t)}{p}} \]
\pagebreak

$ p $
\pagebreak

\[ N(t_i) = \frac{1}{p}\, \sum_{j=i}^{i+p} n_j \]
\pagebreak

$ n_j $
\pagebreak

\[0 \leq t_0 \leq N_{\rm bins}
\]
\pagebreak

\[t_{\rm start} = (\text{fgb} + n_0 - t_0) \times \Delta t
\]
\pagebreak

\[t_{\rm end} = (\text{lgb} - n_1 - t_0) \times \Delta t
\]
\pagebreak

\[t_{\rm start} = (\text{fgb} - t_0) \times \Delta t
\]
\pagebreak

\[t_{\rm end} = (\text{lgb} - t_0) \times \Delta t
\]
\pagebreak

\[\text{scale factor} = \text{packing} \times (t_{\rm res} \times 1000)
\]
\pagebreak

\[\chi^2_{\rm exp} = \sum_{i=t_{\rm start}}^{t_{\rm end}} \frac{[A_{\rm RRF}^{\rm data}(t_i) - A_{\rm RRF}^{\rm theory}(t_i)]^2}{A_{\rm RRF}^{\rm theory}(t_i)}
\]
\pagebreak

\[\mathcal{L} = \prod_i \frac{\mu_i^{n_i} e^{-\mu_i}}{n_i!}
\]
\pagebreak

$\mu_i$
\pagebreak

$n_i$
\pagebreak

\[t_{\rm start} = ({\rm fgb} + n_0 - t_0) \times \Delta t
\]
\pagebreak

\[t_{\rm end} = ({\rm lgb} - n_1 - t_0) \times \Delta t
\]
\pagebreak

\[i_{\rm start} = \lceil \frac{t_{\rm start} - t_{\rm data,0}}{\Delta t_{\rm data}} \rceil
\]
\pagebreak

\[i_{\rm end} = \lfloor \frac{t_{\rm end} - t_{\rm data,0}}{\Delta t_{\rm data}} \rfloor + 1
\]
\pagebreak

$t_{\rm data,0}$
\pagebreak

$\Delta t_{\rm data}$
\pagebreak

\[M(t) = [N(t) - B] \cdot e^{+t/\tau_\mu}
\]
\pagebreak

$\sigma_M = e^{+t/\tau_\mu} \sqrt{N(t) + \sigma_B^2}$
\pagebreak

$w = 1/\sigma_M^2$
\pagebreak

\[A(t) = \frac{M(t)}{N_0} - 1
\]
\pagebreak

\[\sigma_A(t) = \frac{e^{+t/\tau_\mu}}{N_0} \sqrt{N(t) + \left(\frac{N(t)-B}{N_0}\right)^2 \sigma_{N_0}^2}
\]
\pagebreak

\[A_{\rm RRF}(t) = 2 \cdot A(t) \cdot \cos(\omega_{\rm RRF} t + \phi_{\rm RRF})
\]
\pagebreak

$A_{\rm packed} = \frac{1}{n}\sum_{i=1}^{n} A_{\rm RRF}(t_i)$
\pagebreak

$\sigma_{\rm packed} = \frac{\sqrt{2}}{n}\sqrt{\sum_{i=1}^{n} \sigma_A^2(t_i)}$
\pagebreak

\[N_0 = \frac{1}{n} \sum_{i=0}^{n-1} M(t_i)
\]
\pagebreak

\[n_{\rm end} = {\rm round}\left( \left\lceil \frac{T \cdot f_{\rm max}}{2\pi} \right\rceil \cdot \frac{2\pi}{f_{\rm max} \cdot \Delta t} \right)
\]
\pagebreak

\[\sigma_{N_0} = \frac{\sqrt{\sum_{i=0}^{n-1} w_i^2 \sigma_{M_i}^2}}{\sum_{i=0}^{n-1} w_i}
\]
\pagebreak

$ B = \frac{1}{n}\sum_{i={\rm start}}^{{\rm end}} N(i) $
\pagebreak

$ \sigma_B = \sqrt{\frac{1}{n-1}\sum_{i={\rm start}}^{{\rm end}} (N(i) - B)^2} $
\pagebreak

\[ P(t) = c \]
\pagebreak

\[ P(t) = A \]
\pagebreak

\[ P(t) = \exp\left(-\lambda t\right) \]
\pagebreak

\[ P(t) = \exp\left(-\lambda [t-t_{\rm shift}] \right) \]
\pagebreak

\[ P(t) = \exp\left(-[\lambda t]^\beta\right) \]
\pagebreak

\[ P(t) = \exp\left(-[\lambda (t-t_{\rm shift})]^\beta\right) \]
\pagebreak

\[ P(t) = \exp\left(-\frac{1}{2} [\sigma t]^2\right) \]
\pagebreak

\[ P(t) = \exp\left(-\frac{1}{2} [\sigma (t-t_{\rm shift})]^2\right) \]
\pagebreak

\[ P(t) = \frac{1}{3} + \frac{2}{3} \left[1-(\sigma t)^2\right] \exp\left[-\frac{1}{2} (\sigma t)^2\right] \]
\pagebreak

\[ P(t) = \frac{1}{3} + \frac{2}{3} \left[1-(\sigma \{t-t_{\rm shift}\})^2\right] \exp\left[-\frac{1}{2} (\sigma \{t-t_{\rm shift}\})^2\right] \]
\pagebreak

\[ = 1-\frac{2\sigma^2}{(2\pi\nu)^2}\left[1-\exp\left(-1/2 \{\sigma t\}^2\right)\cos(2\pi\nu t)\right] +
    \frac{2\sigma^4}{(2\pi\nu)^3}\int^t_0 \exp\left(-1/2 \{\sigma \tau\}^2\right)\sin(2\pi\nu\tau)\mathrm{d}\tau \]
\pagebreak

$\sigma$
\pagebreak

$\nu$
\pagebreak

$t_{\rm shift}$
\pagebreak

$(\mu\mathrm{s})$
\pagebreak

\[ = \frac{1}{2\pi \imath}\int_{\gamma-\imath\infty}^{\gamma+\imath\infty}
      \frac{f_{\mathrm{G}}(s+\Gamma)}{1-\Gamma f_{\mathrm{G}}(s+\Gamma)} \exp(s t) \mathrm{d}s,
      \mathrm{~where~}\,f_{\mathrm{G}}(s)\equiv \int_0^{\infty}G_{\mathrm{G,LF}}(t)\exp(-s t) \mathrm{d}t\]
\pagebreak

$G_{\mathrm{G,LF}}(t)$
\pagebreak

$\Gamma$
\pagebreak

\[ = 1/3 + 2/3 [1 - \lambda t] \exp(-\lambda t) \]
\pagebreak

$\lambda$
\pagebreak

\[ = 1-\frac{a}{2\pi\nu}j_1(2\pi\nu t)\exp\left(-at\right)-
      \left(\frac{a}{2\pi\nu}\right)^2 \left[j_0(2\pi\nu t)\exp\left(-at\right)-1\right]-
      a\left[1+\left(\frac{a}{2\pi\nu}\right)^2\right]\int^t_0 \exp\left(-a\tau\right)j_0(2\pi\nu\tau)\mathrm{d}\tau) \]
\pagebreak

$a$
\pagebreak

\[ =  \frac{1}{2\pi \imath}\int_{\gamma-\imath\infty}^{\gamma+\imath\infty}
\frac{f_{\mathrm{L}}(s+\Gamma)}{1-\Gamma f_{\mathrm{L}}(s+\Gamma)} \exp(s t) \mathrm{d}s,
\mathrm{~where~}\,f_{\mathrm{L}}(s)\equiv \int_0^{\infty}G_{\mathrm{L,LF}}(t)\exp(-s t) \mathrm{d}t\]
\pagebreak

$G_{\mathrm{L,LF}}(t)$
\pagebreak

\[ \nu_c \gg \gamma_\mu \Delta_{\rm L} \]
\pagebreak

\[ =  1/3 + 2/3 \left(1-(\sigma t)^2-\lambda t\right) \exp\left(-1/2(\sigma t)^2-\lambda t\right)\]
\pagebreak

\[ =  1/3 + 2/3 \left(1-(\sigma t)^\beta \right) \exp\left(-(\sigma t)^\beta / \beta\right)\]
\pagebreak

$\beta$
\pagebreak

\[ = \frac{1}{3}\exp\left(-\sqrt{\frac{4\lambda^2(1-q)t}{\gamma}}\right)+\frac{2}{3}\left(1-\frac{q\lambda^2t^2}{\sqrt{\frac{4\lambda^2(1-q)t}{\gamma}+q\lambda^2t^2}}\right)\exp\left(-\sqrt{\frac{4\lambda^2(1-q)t}{\gamma}+q\lambda^2t^2}\right)\]
\pagebreak

$\gamma$
\pagebreak

$q$
\pagebreak

\[ = \frac{1}{6}\left(1-\frac{\nu t}{2}\right)\exp\left(-\frac{\nu t}{2}\right)+\frac{1}{3}\left(1-\frac{\nu t}{4}\right)\exp\left(-\frac{\nu t + 2.44949\lambda t}{4}\right)\]
\pagebreak

\[ = \exp\left[-\frac{\sigma^2}{\gamma^2}\left(e^{-\gamma t}-1+\gamma t\right)\right] \]
\pagebreak

\[ = \cos(2\pi\nu t + \varphi) \]
\pagebreak

$\varphi$
\pagebreak

\[ = \alpha\,\cos\left(2\pi\nu t+\frac{\pi\varphi}{180}\right)\exp\left(-\lambda_{\mathrm{T}}t\right)+(1-\alpha)\,\exp\left(-\lambda_{\mathrm{L}}t\right)\]
\pagebreak

$\alpha$
\pagebreak

$\lambda_{\rm T}$
\pagebreak

$\lambda_{\rm L}$
\pagebreak

\[ = \alpha\,\left[\cos(2\pi\nu t)-\frac{\sigma^2 t}{2\pi\nu}\sin(2\pi\nu t)\right]\exp(-[\sigma t]^2/2)+(1-\alpha)\,\exp(-(\lambda t)^\beta)\]
\pagebreak

$\alpha=2/3$
\pagebreak

\[ = \alpha\,\left[\cos(2\pi\nu t)-\frac{a}{2\pi\nu}\sin(2\pi\nu t)\right]\exp(-a t)+(1-\alpha)\,\exp(-(\lambda t)^\beta)\]
\pagebreak

\[ = j_0(2\pi\nu t + \varphi) \]
\pagebreak

\[ = \alpha\,j_0\left(2\pi\nu t+\frac{\pi\varphi}{180}\right)\exp\left(-\lambda_{\mathrm{T}}t\right)+(1-\alpha)\,\exp\left(-\lambda_{\mathrm{L}}t\right)\]
\pagebreak

\begin{eqnarray*} &=& \frac{\sigma_{-}}{\sigma_{+}+\sigma_{-}}\exp\left[-\frac{\sigma_{-}^2t^2}{2}\right]
\left\lbrace\cos\left(2\pi\nu t+\frac{\pi\varphi}{180}\right)+
\sin\left(2\pi\nu t+\frac{\pi\varphi}{180}\right)\mathrm{Erfi}\left(\frac{\sigma_{-}t}{\sqrt{2}}\right)\right\rbrace+\\
& & \frac{\sigma_{+}}{\sigma_{+}+\sigma_{-}}
\exp\left[-\frac{\sigma_{+}^2t^2}{2}\right]\left\lbrace\cos\left(2\pi\nu t+\frac{\pi\varphi}{180}\right)-
\sin\left(2\pi\nu t+\frac{\pi\varphi}{180}\right)\mathrm{Erfi}\left(\frac{\sigma_{+}t}{\sqrt{2}}\right)\right\rbrace
\end{eqnarray*}
\pagebreak

$\sigma_{-}$
\pagebreak

$\sigma_{+}$
\pagebreak

$\Delta_{\rm eff}^2 = (1+R_b^2) \Delta_0^2$
\pagebreak

$R_b$
\pagebreak

$\Delta_0$
\pagebreak

$1/\mu\mathrm{sec}$
\pagebreak

\[ = \frac{1}{3} + \frac{2}{3}\,\frac{1}{\left(1+(R_b \Delta_0 t)^2\right)^{3/2}}\,
   \left(1 - \frac{(\Delta_0 t)^2}{\left(1+(R_b \Delta_0 t)^2\right)}\right)\,
   \exp\left[\frac{(\Delta_0 t)^2}{2\left(1+(R_b \Delta_0 t)^2\right)}\right] \]
\pagebreak

$R_{\rm b} = \Delta_{\rm GbG}/\Delta_0$
\pagebreak

\[ = \frac{1}{\sqrt{1+(R_b \gamma\Delta_0 t)^2}}\,
    \exp\left[-\frac{(\gamma\Delta_0 t)^2}{2(1+(R_b \gamma\Delta_0 t)^2)}\right]\,
    \cos(\gamma B_{\rm ext} t + \varphi) \]
\pagebreak

$\nu = \gamma B_{\rm ext}$
\pagebreak

\begin{eqnarray*}\Theta(t) &=& \frac{\exp(-\nu_c t) - 1 - \nu_c t}{\nu_c^2} \\
P_{Z}^{\rm dyn}(t) &=& \sqrt{\frac{1}{1+4 R_b^2 \Delta_0^2 \Theta(t)}}\,\exp\left[-\frac{2 \Delta_0^2 \Theta(t)}{1+4 R_b^2 \Delta_0^2 \Theta(t)}\right]
\end{eqnarray*}
\pagebreak

$\nu_c$
\pagebreak

\begin{eqnarray*}\Theta(t) &=& \frac{\exp(-\nu_c t) - 1 - \nu_c t}{\nu_c^2} \\
P_{X}^{\rm dyn}(t) &=& \sqrt{\frac{1}{1+2 R_b^2 \Delta_0^2 \Theta(t)}}\,\exp\left[-\frac{\Delta_0^2 \Theta(t)}{1+2 R_b^2 \Delta_0^2 \Theta(t)}\right]\,\cos(\gamma B_{\rm ext} t + \varphi)
\end{eqnarray*}
\pagebreak

\[ P(t) = c_0 + c_1 t + c_2 t^2 + c_3 t^3 = \sum_{k=0}^{3} c_k t^k \]
\pagebreak

$c_k$
\pagebreak

$c_0$
\pagebreak

$c_1$
\pagebreak

$c_2$
\pagebreak

$c_3$
\pagebreak

$P(t)$
\pagebreak

\end{document}
