A formula for the k-th covariant derivative

Abstract: The aim of the present paper is to give a formula for the $k$-th covariant derivative of tensor field along a given curve. In order to do that, first the symbols $P^{i<k>}_{j}$ and $Q^{i<k>}_{j}$ which depend on the Christoffel symbols are introduced. Some properties of them are also given. The main result is given by (3.1) and further it is generalized for $k\in R$.