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

• Autorzy: Maciej Szymkat
• Języki publikacji: EN

Abstrakty

PL

Artykuł nie zawiera streszczenia

EN

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.

Słowa kluczowe

EN

Combinatorial identities, bijective combinatorics; Partitions; Ordinary differential operators

• Wydawca: Polish Mathematical Society
• Czasopismo: Mathematica Applicanda
• Rocznik: 1983
• Tom: 11
• Numer: 22

Daty

wydano

1983

online

2016-10-21

Twórcy

autor

Maciej Szymkat

Identyfikatory

DOI

10.14708/ma.v11i22.1591