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Fix formulae of Gamma in command-option doc

This commit is contained in:
Atsushi Togo 2024-09-28 11:27:31 +09:00
parent 26602a73db
commit d8490c88c6
1 changed files with 9 additions and 9 deletions
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18
doc/command-options.md
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@ -626,9 +626,9 @@ $$
\bigl|\Phi_{-\lambda\lambda'\lambda''}\bigl|^2
\left\{(n_{\lambda'}+ n_{\lambda''}+1)
\delta(\omega-\omega_{\lambda'}-\omega_{\lambda''}) \right.
* (n_{\lambda'}-n_{\lambda''})
+ (n_{\lambda'}-n_{\lambda''})
\left[\delta(\omega+\omega_{\lambda'}-\omega_{\lambda''})
* \left. \delta(\omega-\omega_{\lambda'}+\omega_{\lambda''})
- \left. \delta(\omega-\omega_{\lambda'}+\omega_{\lambda''})
\right]\right\}.
$$
@ -858,7 +858,7 @@ $$
\bigl|\Phi_{-\lambda\lambda_1\lambda_2}\bigl|^2
(n_{\lambda_1}-n_{\lambda_2})
\left[\delta(\omega+\omega_{\lambda_1}-\omega_{\lambda_2})
* \delta(\omega-\omega_{\lambda_1}+\omega_{\lambda_2})
- \delta(\omega-\omega_{\lambda_1}+\omega_{\lambda_2})
\right]
\end{align*}
$$
@ -872,7 +872,7 @@ $$
\bigl|\Phi_{-\lambda\lambda_1\lambda_2}\bigl|^2
(n_{\lambda_1}+ n_{\lambda_2}+1)
\left[ \delta(\omega-\omega_{\lambda_1}-\omega_{\lambda_2})
* \delta(\omega + \omega_{\lambda_1} + \omega_{\lambda_2}) \right]
- \delta(\omega + \omega_{\lambda_1} + \omega_{\lambda_2}) \right]
\end{align*},
$$
@ -940,11 +940,11 @@ $$
\bigl|\Phi_{-\lambda\lambda_1\lambda_2}\bigl|^2 &
\left\{(n_{\lambda_1}+ n_{\lambda_2}+1)
\left[ \delta(\omega-\omega_{\lambda_1}-\omega_{\lambda_2})
* \delta(\omega+\omega_{\lambda_1}+\omega_{\lambda_2}) \right] \right.
- \delta(\omega+\omega_{\lambda_1}+\omega_{\lambda_2}) \right] \right.
\\
& + (n_{\lambda_1}-n_{\lambda_2})
\left[\delta(\omega+\omega_{\lambda_1}-\omega_{\lambda_2})
* \left. \delta(\omega-\omega_{\lambda_1}+\omega_{\lambda_2})
- \left. \delta(\omega-\omega_{\lambda_1}+\omega_{\lambda_2})
\right]\right\},
\end{align*}
$$
@ -959,14 +959,14 @@ $$
\left\{
\left[ \frac{(n_{\lambda_1}+ n_{\lambda_2}+1)}{
(\omega-\omega_{\lambda_1}-\omega_{\lambda_2})_\mathrm{p}}
* \frac{(n_{\lambda_1}+ n_{\lambda_2}+1)}{
- \frac{(n_{\lambda_1}+ n_{\lambda_2}+1)}{
(\omega+\omega_{\lambda_1}+\omega_{\lambda_2})_\mathrm{p}}
\right]
\right. \\
& + \left[
\frac{(n_{\lambda_1}-n_{\lambda_2})}{(\omega +
\omega_{\lambda_1} - \omega_{\lambda_2})_\mathrm{p}}
* \left. \frac{(n_{\lambda_1}-n_{\lambda_2})}{(\omega -
- \left. \frac{(n_{\lambda_1}-n_{\lambda_2})}{(\omega -
\omega_{\lambda_1} + \omega_{\lambda_2})_\mathrm{p}}
\right]\right\},
\end{align*}
@ -1030,7 +1030,7 @@ A_\lambda(\omega) = \frac{1}{\pi} \frac{4\Omega^2_\lambda
\Gamma_\lambda(\omega)}
{\left[\omega^2 - \Omega^2_\lambda -
2\Omega_\lambda \Delta_\lambda(\omega) \right]^2
* \left[ 2\Omega_\lambda
- \left[ 2\Omega_\lambda
\Gamma_\lambda(\omega) \right]^2},
$$