448 research outputs found
Some identities of higher-order Bernoulli, Euler and Hermite polynomials arising from umbral calculus
In this paper, we study umbral calculus to have alternative ways of obtaining
our results. That is, we derive some interesting identities of the higher-order
Bernoulli, Euler and Hermite polynomials arising from umbral calculus to have
alternative ways.Comment: 10 page
On some applications of a symbolic representation of non-centered L\'evy processes
By using a symbolic technique known in the literature as the classical umbral
calculus, we characterize two classes of polynomials related to L\'evy
processes: the Kailath-Segall and the time-space harmonic polynomials. We
provide the Kailath-Segall formula in terms of cumulants and we recover simple
closed-forms for several families of polynomials with respect to not centered
L\'evy processes, such as the Hermite polynomials with the Brownian motion, the
Poisson-Charlier polynomials with the Poisson processes, the actuarial
polynomials with the Gamma processes, the first kind Meixner polynomials with
the Pascal processes, the Bernoulli, Euler and Krawtchuk polynomials with
suitable random walks
Some aspects of Fibonacci polynomial congruences
This paper formulates a definition of Fibonacci polynomials which is
slightly different from the traditional definitions, but which is related to the
classical polynomials of Bernoulli, Euler and Hermite. Some related congruence
properties are developed and some unanswered questions are outlined.
Keywords: Congruences, recurrence relations, Fibonacci sequence, Lucas sequences,
umbral calculus
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