Results 11 to 20 of about 142 (36)
Blissard's trigonometric series with closed-form sums [PDF]
arXiv, 2020 This is a summary and verification of an elementary note written by John Blissard in 1862 for the Messenger of Mathematics. A general method of discovering trigonometric series having a closed-form sum is explained and illustrated with examples.
arxiv
Some identities involving Appell polynomials [PDF]
arXiv, 2017 In this papier, by the classical umbral calculus method, we establish identities involving the Appell polynomials and extend some existing identities.
arxiv
arXiv, 1995 We characterize those linear operators that can be expressed as a sum over k of terms of the form f_k(D) x^k and give several examples.
arxiv
Maple umbral calculus package [PDF]
arXiv, 1995 We are developing a Maple package of functions related to Rota's Umbral Calculus. A Mathematica version of this package is being developed in parallel.
arxiv
Umbral presentations for polynomial sequences [PDF]
arXiv, 1999 Using random variables as motivation, this paper presents an exposition of the formalisms developed by Rota and Taylor for the classical umbral calculus. A variety of examples are presented, culminating in several descriptions of sequences of binomial type in terms of umbral polynomials.
arxiv
q-Poisson, q-Dobinski, q-Rota and q-coherent states [PDF]
Proc. Jangjeon Math. Soc. Vol. 7 (2), 2004 pp. 95-98, 2004 q- Dobinski formula may be interpreted as the average of powers of a random variable X_q with the q- Poisson distribution.
arxiv
Umbral Calculus in Positive Characteristic [PDF]
arXiv, 2004 An umbral calculus over local fields of positive characteristic is developed on the basis of a relation of binomial type satisfied by the Carlitz polynomials. Orthonormal bases in the space of continuous $\mathbb F_q$-linear functions are constructed.
arxiv
The logarithmic fibbinomial formula [PDF]
Adv. Stud. Contemp. Math. v.9 No.1 (2004) 19-26, 2004 Roman logarithmic binomial formula analogue has been found . It is presented here also for the case of fibonomial coefficients which recently have been given a combinatorial interpretation by the present author.
arxiv
Some applications of degenerate poly-Bernoulli numbers and polynomials [PDF]
arXiv, 2015 In this paper, we consider degenerate poly-Bernoulli numbers and polynomials associated with polylogarithmic function and p-adic invariant integral on Zp.
arxiv
On central Fubini-like numbers and polynomials [PDF]
arXiv, 2018 We introduce the central Fubini-like numbers and polynomials using Rota approach. Several identities and properties are established as generating functions, recurrences, explicit formulas, parity, asymptotics and determinantal representation.
arxiv