Geodesic
The Leibniz formula for the covariant derivative and some of its applications
Matematičeskie trudy, Tome 13 (2010) no. 1, pp. 63-84.

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We obtain a formula for the higher covariant derivatives on the tensor product of vector bundles which is a wide generalization of the classical Leibniz formula. We construct an algorithm for the calculation of the part of the Taylor series of the double exponential map linear with respect to the second variable. 
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A. V. Gavrilov. The Leibniz formula for the covariant derivative and some of its applications. Matematičeskie trudy, Tome 13 (2010) no. 1, pp. 63-84. http://geodesic.mathdoc.fr/item/MT_2010_13_1_a3/

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