viernes, 4 de septiembre de 2020

geodesiques

R^{k}_{i_{1}...i_{n}}·d_{t}[x_{i_{1}}(t)]·...·d_{t}[x_{i_{n}}(t)] = d_{t...t}^{n}[x_{k}(t)]


x_{k}(t) = t^{k}

R^{k}_{i_{1}...i_{n}} = ( 1/(i_{1}...i_{n}) )·( k!/(k+(-n))! )·t^{k+(-1)·(i_{1}+...+i_{n})}


x_{k}(t) = e^{k·t}

R^{k}_{i_{1}...i_{n}} = ( 1/(i_{1}...i_{n}) )·( k^{n} )·e^{(k+(-1)·(i_{1}+...+i_{n}))·t}


x_{k}(t) = ln(t^{k})

R^{k}_{i_{1}...i_{n}} = ( 1/(i_{1}...i_{n}) )·( (-1)^{n+1}·k·n! )

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