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Dmitry V. Dolgy

Publications and source records attributed to Dmitry V. Dolgy.

11 recordsLinked to original sources
arXiv2025

A note on new type degenerate Srirling numbers of the first kind

We introduce a new sequence of unsigned degenerate Stirling numbers of the first kind. Following the work of Adell-Lekuona, who represented unsigned Stirling numbers of the first kind as multiples of the expectations of specific random variables, we express our new numbers as finite sums of multiples of the expectations of certain random variables. We also provide a representation of these new numbers as finite sums involving the classical unsigned Stirling numbers of the first kind. As an inversion formula, we define a corresponding sequence of new type degenerate Stirling numbers of the second kind. We derive expressions for these numbers as finite sums that involve the Stirling numbers of the second kind.

math.NT↗
arXiv2021

A note on degenerate generalized Laguerre polynomials and Lah numbers

The aim of this paper is to introduce the degenerate generalized Laguerre polynomials as the degenerate version of the generalized Laguerre polynomials and to derive some properties related to those polynomials and Lah numbers, including an explicit expression, a Rodrigues' type formula and expressions for the derivatives. The novelty of the present paper is that it is the first paper on degenerate versions of orthogonal polynomials.

math.CA↗
arXiv2021

A new approach to Bell and poly-Bell numbers and polynomials

The aim of this paper is to introduce Bell polynomials and numbers of the second kind and poly-Bell polynomials and numbers of the second kind, and to derive their explicit expressions, recurrence relations and some identities involving those polynomials and numbers. We also consider degenerate versions of those polynomials and numbers, namely degenerate Bell polynomials and numbers of the second kind and degenerate poly-Bell polynomials and numbers of the second kind, and deduce their similar results.

math.NT↗
arXiv2019

Some identities on r-central factorial numbers and r-central Bell polynomials

In this paper, we introduce the extended r-central factorial numbers of the second and first kinds and the extended r-central Bell polynomials, as extended versions and central analogues of some previously introduced numbers and polynomials. Then we study various properties and identities related to these numbers and polynomials and also their connections.

math.NT↗
arXiv2016

Convolved Fibonacci Numbers and their applications

In this paper, we present a new approach to the convolved Fibonacci numbers arising from the generating function of them and give some new and explicit identities for the convolved Fibonacci numbers.

math.NT↗
arXiv2016

Differential equations for Changhee polynomials and their applications

Recently, the non-linear Changhee differential equations were introduced in [5] and these differential equations turned out to be very useful for studying special polynomials and mathematical physics. Some interesting identities and properties of Changhee polynomials can also be derived from umbral calculus (see [7]). In this paper, we consider differential equations arising from Changhee polynomials and derive some new and explicit formulae and identities from our differential equations.

math.NT↗
arXiv2015

On degenerate q-Euler polynomials

In this paper, we consider degenerate Carlitz's type q-Euler polynmials and numbers and we investigate some identities arising from the fermionic p-adic integral equations and the generating function of thoe polynomials.

math.NT↗
arXiv2015

Some identities of q-Bernoulli polynomials under symmetry group S3

In this paper, we give some new identities of Carlitz q-Bernoulli polynomials under symmetry group S 3 . The derivatives of identities are based on the q-Volkenborn integral expression of the generating function for the Carlitz q-Bernoulli polynomials and the q-Volkenborn integral equations that can be expressed as the exponential generating functions for the q-power sums.

math.NT↗
arXiv2013

Sheffer sequences of polynomials and their applications

In this paper, we investigate some properties of several Sheffer sequences of several polynomials arising from umbral calculus. From our investigation, we can derive many interesting identities of several polynomials

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