Results 31 to 36 of about 142 (36)

An umbral setting for cumulants and factorial moments [PDF]

arXiv, 2004
We provide an algebraic setting for cumulants and factorial moments through the classical umbral calculus. Main tools are the compositional inverse of the unity umbra, connected with the logarithmic power series, and a new umbra here introduced, the singleton umbra.
arxiv  

A symbolic method for k-statistics [PDF]

arXiv, 2005
Trough the classical umbral calculus, we provide new, compact and easy to handle expressions of k-statistics, and more in general of U-statistics. In addition such a symbolic method can be naturally extended to multivariate case and to generalized k-statistics.
arxiv  

Set maps, umbral calculus, and the chromatic polynomial [PDF]

arXiv, 2005
Some important properties of the chromatic polynomial also hold for any polynomial set map satisfying p_S(x+y)=\sum_{T\uplus U=S}p_T(x)p_U(y). Using umbral calculus, we give a formula for the expansion of such a set map in terms of any polynomial sequence of binomial type. This leads to some new expansions of the chromatic polynomial.
arxiv  

A note on some identities of derangement polynomials. [PDF]

J Inequal Appl, 2018
Kim T, Kim DS, Jang GW, Kwon J.
europepmc   +1 more source

Korobov polynomials of the third kind and of the fourth kind. [PDF]

Springerplus, 2015
Kim T, Kim DS.
europepmc   +1 more source

Extended finite operator calculus—an example of algebraization of analysis

Open Mathematics, 2004
Kwaśniewski Andrzej, Borak Ewa
doaj   +1 more source