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ART-Skript Eq: math.1110.188

Hash: 07d8c33ff4515e35258e6c7a14391315

TeX (original user input):

\begin{align}
  & \begin{array}{*{35}{l}}
   T_{rs...;l}^{ik...}=T_{rs...,l}^{ik...} & +\Gamma _{ml}^{i}T_{rs...}^{mk...}\quad  & {} & +\Gamma _{ml}^{k}T_{rs...}^{im...}... & \quad  & \text{f }\!\!\ddot{\mathrm{u}}\!\!\text{ r jeden oberen Index}  \\
   {} & -\Gamma _{rl}^{m}T_{ms...}^{ik...}\quad  & {} & -\Gamma _{sl}^{m}T_{rm...}^{ik...}... & {} & \text{f }\!\!\ddot{\mathrm{u}}\!\!\text{ r jeden unteren Index}  \\
\end{array} \\
 & \begin{matrix}
   T_{rs...;l}^{ik...}=T_{rs...,l}^{ik...} & +\Gamma _{ml}^{i}T_{rs...}^{mk...} & +\Gamma _{ml}^{k}T_{rs...}^{im...}... & \text{f }\!\!\ddot{\mathrm{u}}\!\!\text{ r jeden oberen Index}  \\
   {} & -\Gamma _{rl}^{m}T_{ms...}^{ik...} & -\Gamma _{sl}^{m}T_{rm...}^{ik...}... & \text{f }\!\!\ddot{\mathrm{u}}\!\!\text{ r jeden unteren Index}  \\
\end{matrix} \\
\end{align}

TeX (checked):

{\begin{aligned}&{\begin{array}{*{35}{l}}T_{rs...;l}^{ik...}=T_{rs...,l}^{ik...}&+\Gamma _{ml}^{i}T_{rs...}^{mk...}\quad &{}&+\Gamma _{ml}^{k}T_{rs...}^{im...}...&\quad &{\text{f }}\!\!{\ddot {\mathrm {u} }}\!\!{\text{ r jeden oberen Index}}\\{}&-\Gamma _{rl}^{m}T_{ms...}^{ik...}\quad &{}&-\Gamma _{sl}^{m}T_{rm...}^{ik...}...&{}&{\text{f }}\!\!{\ddot {\mathrm {u} }}\!\!{\text{ r jeden unteren Index}}\\\end{array}}\\&{\begin{matrix}T_{rs...;l}^{ik...}=T_{rs...,l}^{ik...}&+\Gamma _{ml}^{i}T_{rs...}^{mk...}&+\Gamma _{ml}^{k}T_{rs...}^{im...}...&{\text{f }}\!\!{\ddot {\mathrm {u} }}\!\!{\text{ r jeden oberen Index}}\\{}&-\Gamma _{rl}^{m}T_{ms...}^{ik...}&-\Gamma _{sl}^{m}T_{rm...}^{ik...}...&{\text{f }}\!\!{\ddot {\mathrm {u} }}\!\!{\text{ r jeden unteren Index}}\\\end{matrix}}\\\end{aligned}}

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\begin{aligned} \begin{array}{l} T_{r s . . .; l}^{i k . . .} = T_{r s . . ., l}^{i k . . .} & + Γ_{m l}^{i} T_{r s . . .}^{m k . . .} & + Γ_{m l}^{k} T_{r s . . .}^{i m . . .} . . . & f \ddot{u} r jeden oberen Index \\ - Γ_{r l}^{m} T_{m s . . .}^{i k . . .} & - Γ_{s l}^{m} T_{r m . . .}^{i k . . .} . . . & f \ddot{u} r jeden unteren Index \end{array} \\ \begin{matrix} T_{r s . . .; l}^{i k . . .} = T_{r s . . ., l}^{i k . . .} & + Γ_{m l}^{i} T_{r s . . .}^{m k . . .} & + Γ_{m l}^{k} T_{r s . . .}^{i m . . .} . . . & f \ddot{u} r jeden oberen Index \\ - Γ_{r l}^{m} T_{m s . . .}^{i k . . .} & - Γ_{s l}^{m} T_{r m . . .}^{i k . . .} . . . & f \ddot{u} r jeden unteren Index \end{matrix} \end{aligned}

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In Mathematica:

Identifiers

$T$

$r$

$s$

$l$

$i$

$k$

$T$

$r$

$s$

$l$

$i$

$k$

$Γ$

$m$

$l$

$i$

$T$

$r$

$s$

$m$

$k$

$Γ$

$m$

$l$

$k$

$T$

$r$

$s$

$i$

$m$

$\ddot{u}$

$Γ$

$r$

$l$

$m$

$T$

$m$

$s$

$i$

$k$

$Γ$

$s$

$l$

$m$

$T$

$r$

$m$

$i$

$k$

$\ddot{u}$

$T$

$r$

$s$

$l$

$i$

$k$

$T$

$r$

$s$

$l$

$i$

$k$

$Γ$

$m$

$l$

$i$

$T$

$r$

$s$

$m$

$k$

$Γ$

$m$

$l$

$k$

$T$

$r$

$s$

$i$

$m$

$\ddot{u}$

$Γ$

$r$

$l$

$m$

$T$

$m$

$s$

$i$

$k$

$Γ$

$s$

$l$

$m$

$T$

$r$

$m$

$i$

$k$

$\ddot{u}$

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