[itex](V(s)_{||})^\mu = V(s)^\mu + s \Gamma^\mu_{\nu \lambda} \frac{dx^\nu}{ds} V(s)^\lambda + [/itex] higher-order terms(adsbygoogle = window.adsbygoogle || []).push({});

(Here we have parallel transported vector from point "s" to a very close point)

Hi, I tried to make some calculations to reach the high-order terms for parallel transporting of vector above and I think they may be shaky, so I would like to ask it on forum about how these high-order terms are expanded?? what is the logic of expanding high order terms??? Could you show the expansion of high- order terms using mathematical stuff or approach??? I tried to make some search on internet but have not obtained any valuable information.

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# A Expansion of covariant derivative

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