Geodesic
The form of the n-th iteration of the operator q=fd/dx
Mathematica Applicanda, Tome 11 (1983) no. 22, pp. 227-249.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

Motivated by applications in linear dynamical systems, the author studies q^n(f), where q is the operator f●(d/dx) and qn is its n-th iteration. q^n(f) is a polynomial F(f(0),f(1),...,f(n)) in the derivatives f(0)=f,...,f(n) of f with integer coefficients. Special attention is paid to determining the coefficients of F. The author presents algorithms for computing the coefficients and also shows that the sum of all coefficients of F equals n!. The paper ends with some remarks on the number of coefficients of F, which is related to the number-theoretic unrestricted partition function.
DOI : 10.14708/ma.v11i22.1591
Classification : 05A19 (10A45 47E05)
Mots-clés : Combinatorial identities, bijective combinatorics, Partitions, Ordinary differential operators 
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Maciej Szymkat. The form of the n-th iteration of the operator q=fd/dx. Mathematica Applicanda, Tome 11 (1983) no. 22, pp.  227-249. doi : 10.14708/ma.v11i22.1591. http://geodesic.mathdoc.fr/articles/10.14708/ma.v11i22.1591/

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