Geodesic
On the Peano Derivatives
Canadian journal of mathematics, Tome 25 (1973) no. 1, pp. 127-140

Voir la notice de l'article provenant de la source Cambridge University Press

Let f be a real valued function defined in some neighbourhood of a point x. If there are numbers α 1, α 2, ... α r-1, independent of h such that then the number αk is called the kth Peano derivative (also called kth de la Vallée Poussin derivative [6]) of f at x and we write αk = fk(x). It is convenient to write α 0 = f 0(x) = f(x). The definition is such that if the mth Peano derivative exists so does the nth for 0 ≦ n ≦ m. 
Bullen, P. S.; Mukhopadhyay, S. N. On the Peano Derivatives. Canadian journal of mathematics, Tome 25 (1973) no. 1, pp. 127-140. doi: 10.4153/CJM-1973-012-7
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