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S=\bigcup_{i=0}^{i_{0}}S_{i}. |
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\sum_{i=0}^{d-1}\beta_{i}f_{i}=0 |
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\sum_{i=0}^{d-1}\beta_{i}f_{i}(w_{j})=0. |
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\sum_{i=0}^{m-1}\beta_{i}f_{\rho^{i}(q)}=0 |
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a(n)=\xi_{m}^{e_{k:v}(n)}, |
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C(x,y)=\sum_{m=0}^{c}C_{m}(x)y^{m}, |
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\eta_{j}=\sum_{i=0}^{s_{0}-1}\omega^{jk^{i}}. |
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\prod_{j=0}^{q-1}C(x^{u_{j}},y)=\sum_{m=0}^{qc}D_{m}(x)y^{m}. |
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\displaystyle\sigma_{pn}(\lambda) |
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\sum_{m=0}^{qc}D_{m}(\omega)A(k^{ms}n;\omega)=0 |
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\displaystyle x^{2^{s+1}-1}T\left(2^{s+1};\frac{1}{x}\right) |
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p=(T(2^{s_{0}};\omega))^{q}, |
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1=\Phi_{r_{0}}(1)=|T(2^{s_{0}};\omega)|^{2}, |
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(-1)^{s_{0}/2}=[\omega T(2^{s_{0}/2},\omega)]^{2}. |
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(\omega T(2^{s_{0}/2};\omega)-1)(\omega T(2^{s_{0}/2};\omega)+1)=0. |
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\displaystyle m_{ij}(k^{t+1};x) |
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M_{vw}=M_{v}M_{w}. |
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f(vw)=M_{v}f(w) |
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\displaystyle 0,n>1; |
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F(n;x)=[F_{0}(n;x),\ldots,F_{d-1}(n;x)]^{T}. |
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\displaystyle F(k^{u+t};x) |
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\displaystyle F^{R}(k^{u+t};x) |
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\displaystyle F_{i}(k^{u+1};x) |
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\displaystyle=\sum_{j=0}^{d-1}m_{ij}(x^{k^{u}})F_{j}(k^{u};x) |
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\displaystyle=\sum_{j=0}^{c}\widehat{m}_{ij}(x^{k^{u}})F_{j}(k^{u};x), |
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\widehat{F}(k^{u+t};x)=\widehat{M}(k^{t};x^{k^{u}})\widehat{F}(k^{u};x). |
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\widehat{F}(k^{ms};\omega)=\widehat{M}^{m}(k^{s};\omega)\widehat{F}(1;\omega). |
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\sum_{m=0}^{l}C_{m}(\omega)\widehat{F}(k^{ms};\omega)=0. |
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\sum_{m=0}^{l}C_{m}(\omega)\widehat{F}(k^{ms}n;\omega)=0. |
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\displaystyle\sigma_{p1}(\lambda) |
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\sum_{m=0}^{l}C_{m}(\omega)\widehat{F}^{R}(k^{ms}n;\omega)=0. |
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\rho(p,t)=(p+1\bmod{m},t). |
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f_{\rho(q)}=\xi_{m}f_{q}, |
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\displaystyle\widehat{M}(k^{s};\omega) |
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\displaystyle\widehat{M}(k^{s};\omega^{k}) |
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\sum_{m=0}^{qc}D_{m}(\omega)A(k^{ms}n;\omega)=0. |
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\displaystyle T(J_{\mu}(x/2)J_{\nu}(-x/2)) |
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\displaystyle O^{q}(\kappa_{1},\kappa_{2}) |
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\displaystyle O^{G}(\kappa_{1},\kappa_{2}) |
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\displaystyle O^{q}_{\rm 5}(\kappa_{1},\kappa_{2}) |
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\displaystyle\sigma_{1}(\lambda)\Theta(\lambda-Q); |
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\displaystyle O^{G}_{\rm 5}(\kappa_{1},\kappa_{2}) |
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\displaystyle\frac{\langle p_{1}|O^{i}|p_{2}\rangle}{(i\tilde{x}p_{+})^{h_{i}}} |
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\displaystyle\langle p_{1}|O^{i}|p_{2}\rangle\cdot(\kappa_{-})^{h_{i}} |
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h_{q}=1,~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}h_{G}=2~{}. |
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\displaystyle\mu^{2}\frac{d}{d\mu^{2}}O^{i}(\kappa_{1},\kappa_{2}) |
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\displaystyle K^{qq}(\alpha_{1},\alpha_{2}) |
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\displaystyle K^{qG}(\alpha_{1},\alpha_{2}) |
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\displaystyle K^{Gq}(\alpha_{1},\alpha_{2}) |
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\displaystyle K^{GG}(\alpha_{1},\alpha_{2}) |
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\displaystyle C_{A}\left\{4(1-\alpha_{1}-\alpha_{2})+12\alpha_{1}\alpha_{2}\right. |
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\displaystyle\sigma_{h1}(\lambda) |
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\displaystyle\Delta K^{qq}(\alpha_{1},\alpha_{2}) |
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\displaystyle K^{qq}(\alpha_{1},\alpha_{2}), |
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\displaystyle\Delta K^{qG}(\alpha_{1},\alpha_{2}) |
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\displaystyle-2N_{f}T_{R}\kappa_{-}\left\{1-\alpha_{1}-\alpha_{2}\right\}, |
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\displaystyle\Delta K^{Gq}(\alpha_{1},\alpha_{2}) |
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\displaystyle\Delta K^{GG}(\alpha_{1},\alpha_{2}) |
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\displaystyle K^{GG}(\alpha_{1},\alpha_{2})-12C_{A}\alpha_{1}\alpha_{2}~{}. |
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\displaystyle D\alpha |
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\displaystyle\mu^{2}\frac{d}{d\mu^{2}}G^{i}(z_{+},z_{-}) |
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\displaystyle\Phi_{i}(t,\tau) |
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\displaystyle\sigma_{1}(\lambda)\Theta(Q-\lambda). |
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\displaystyle\int_{-\infty}^{+\infty}dz_{-}F_{i}(t-\tau z_{-},z_{-}), |
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\displaystyle F_{i}(z_{+},z_{-}) |
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\displaystyle\mu^{2}\frac{d}{d\mu^{2}}\Phi^{i}(t,\tau) |
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\displaystyle V_{ext}^{ij}(t,t^{\prime},\tau) |
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\displaystyle V^{qq}_{ext}(t,t^{\prime},\tau) |
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\displaystyle V^{qG}_{ext}(t,t^{\prime},\tau) |
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\displaystyle V^{Gq}_{ext}(t,t^{\prime},\tau) |
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\displaystyle V^{GG}_{ext}(t,t^{\prime},\tau) |
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\displaystyle+\frac{1}{4\tau}\beta_{0}\delta(x-y) |
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\displaystyle\Delta V^{qq}_{ext}(t,t^{\prime},\tau) |
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\displaystyle\log(f(\epsilon_{\lambda n}(\lambda))) |
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\displaystyle\Delta V^{qG}_{ext}(t,t^{\prime},\tau) |
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\displaystyle\Delta V^{Gq}_{ext}(t,t^{\prime},\tau) |
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\displaystyle\Delta V^{GG}_{ext}(t,t^{\prime},\tau) |
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\displaystyle+\frac{1}{4\tau}\beta_{0}\delta(x-y), |
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\displaystyle V^{qq}(x,y) |
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\displaystyle C_{F}\left[\frac{x}{y}-\frac{1}{y}+\frac{1}{(y-x)_{+}}\right] |
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\displaystyle V^{qG}(x,y) |
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\displaystyle-2N_{f}T_{R}\frac{x}{y}\left[4(1-x)+\frac{1-2x}{y}\right] |
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\displaystyle V^{Gq}(x,y) |
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\displaystyle C_{F}\left[1-\frac{x^{2}}{y}\right] |