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

Mathematica Applicanda (1983)

- Volume: 11, Issue: 22
- ISSN: 1730-2668

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topMaciej 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 -

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