The form of the n-th iteration of the operator q=fd/dx

Maciej Szymkat. "The form of the n-th iteration of the operator q=fd/dx." Mathematica Applicanda 11.22 (1983): null. <http://eudml.org/doc/292760>.

@article{MaciejSzymkat1983,
abstract = {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.},
author = {Maciej Szymkat},
journal = {Mathematica Applicanda},
keywords = {Combinatorial identities, bijective combinatorics; Partitions; Ordinary differential operators},
language = {eng},
number = {22},
pages = {null},
title = {The form of the n-th iteration of the operator q=fd/dx},
url = {http://eudml.org/doc/292760},
volume = {11},
year = {1983},
}

TY - JOUR
AU - Maciej Szymkat
TI - The form of the n-th iteration of the operator q=fd/dx
JO - Mathematica Applicanda
PY - 1983
VL - 11
IS - 22
SP - null
AB - 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.
LA - eng
KW - Combinatorial identities, bijective combinatorics; Partitions; Ordinary differential operators
UR - http://eudml.org/doc/292760
ER -