Results 1 to 10 of about 73 (47)
Umbral Methods and Harmonic Numbers
Axioms, 2018 The theory of harmonic-based functions is discussed here within the framework of umbral operational methods. We derive a number of results based on elementary notions relying on the properties of Gaussian integrals.
Silvia Licciardi +2 more
exaly +3 more sources
Fully degenerate poly-Bernoulli numbers and polynomials
Open Mathematics, 2016 In this paper, we introduce the new fully degenerate poly-Bernoulli numbers and polynomials and inverstigate some properties of these polynomials and numbers.
Taekyun Kim, Jong-Jin Seo
exaly +2 more sources
Apostol-Euler polynomials arising from umbral calculus [PDF]
Advances in Differential Equations, 2013 In this paper, by using the orthogonality type as defined in the umbral calculus, we derive an explicit formula for several well-known polynomials as a linear combination of the Apostol-Euler polynomials.MSC:05A40.
Taekyun Kim +3 more
semanticscholar +2 more sources
Open Mathematics, 2023 Hyperharmonic numbers were introduced by Conway and Guy (The Book of Numbers, Copernicus, New York, 1996), whereas harmonic numbers have been studied since antiquity.
Kim Taekyun, Kim Dae San, Kim Hye Kyung
doaj +1 more source
Barnes-type Daehee polynomials [PDF]
Advances in Differential Equations, 2014 In this paper, we consider Barnes-type Daehee polynomials of the first kind and of the second kind. From the properties of the Sheffer sequences of these polynomials arising from umbral calculus, we derive new and interesting identities.MSC:05A15, 05A40,
Dae San Kim +3 more
semanticscholar +2 more sources
Representations by degenerate Daehee polynomials
Open Mathematics, 2022 In this paper, we consider the problem of representing any polynomial in terms of the degenerate Daehee polynomials and more generally of the higher-order degenerate Daehee polynomials.
Kim Taekyun +3 more
doaj +1 more source
q-Functions and Distributions, Operational and Umbral Methods
Mathematics, 2021 The use of non-standard calculus means have been proven to be extremely powerful for studying old and new properties of special functions and polynomials.
Giuseppe Dattoli +3 more
doaj +1 more source
Study of degenerate derangement polynomials by λ-umbral calculus
Demonstratio Mathematica, 2023 In the 1970s, Rota began to build completely rigid foundations for the theory of umbral calculus based on relatively modern ideas of linear functions and linear operators.
Yun Sang Jo, Park Jin-Woo
doaj +1 more source
Sheffer sequences of polynomials and their applications [PDF]
Advances in Differential Equations, 2013 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.MSC:05A40, 05A19.
Dae San Kim +3 more
semanticscholar +2 more sources
Barnes’ multiple Frobenius-Euler and poly-Bernoulli mixed-type polynomials
Advances in Differential Equations, 2014 In this paper, we consider Barnes’ multiple Frobenius-Euler and poly-Bernoulli mixed-type polynomials. From the properties of Sheffer sequences of these polynomials arising from umbral calculus, we derive new and interesting identities.MSC:05A15, 05A40 ...
Dae San Kim +3 more
semanticscholar +2 more sources