On the type 2 poly-Bernoulli polynomials associated with umbral calculus

Type 2 poly-Bernoulli polynomials were introduced recently with the help of modified polyexponential functions. In this paper, we investigate several properties and identities associated with those polynomials arising from umbral calculus techniques. In particular, we express the type 2 poly-Bernoul...

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Autores principales:	Kim Taekyun, Kim Dae San, Dolgy Dmitry V., Park Jin-Woo
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	type 2 poly-bernoulli polynomials umbral calculus modified poly-exponential functions 11b83 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/e8d9e0b6159a4953844890d2eaa01437
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spelling	oai:doaj.org-article:e8d9e0b6159a4953844890d2eaa014372021-12-05T14:10:53ZOn the type 2 poly-Bernoulli polynomials associated with umbral calculus2391-545510.1515/math-2021-0086https://doaj.org/article/e8d9e0b6159a4953844890d2eaa014372021-08-01T00:00:00Zhttps://doi.org/10.1515/math-2021-0086https://doaj.org/toc/2391-5455Type 2 poly-Bernoulli polynomials were introduced recently with the help of modified polyexponential functions. In this paper, we investigate several properties and identities associated with those polynomials arising from umbral calculus techniques. In particular, we express the type 2 poly-Bernoulli polynomials in terms of several special polynomials, like higher-order Cauchy polynomials, higher-order Euler polynomials, and higher-order Frobenius-Euler polynomials.Kim TaekyunKim Dae SanDolgy Dmitry V.Park Jin-WooDe Gruyterarticletype 2 poly-bernoulli polynomialsumbral calculusmodified poly-exponential functions11b83MathematicsQA1-939ENOpen Mathematics, Vol 19, Iss 1, Pp 878-887 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	type 2 poly-bernoulli polynomials umbral calculus modified poly-exponential functions 11b83 Mathematics QA1-939
spellingShingle	type 2 poly-bernoulli polynomials umbral calculus modified poly-exponential functions 11b83 Mathematics QA1-939 Kim Taekyun Kim Dae San Dolgy Dmitry V. Park Jin-Woo On the type 2 poly-Bernoulli polynomials associated with umbral calculus
description	Type 2 poly-Bernoulli polynomials were introduced recently with the help of modified polyexponential functions. In this paper, we investigate several properties and identities associated with those polynomials arising from umbral calculus techniques. In particular, we express the type 2 poly-Bernoulli polynomials in terms of several special polynomials, like higher-order Cauchy polynomials, higher-order Euler polynomials, and higher-order Frobenius-Euler polynomials.
format	article
author	Kim Taekyun Kim Dae San Dolgy Dmitry V. Park Jin-Woo
author_facet	Kim Taekyun Kim Dae San Dolgy Dmitry V. Park Jin-Woo
author_sort	Kim Taekyun
title	On the type 2 poly-Bernoulli polynomials associated with umbral calculus
title_short	On the type 2 poly-Bernoulli polynomials associated with umbral calculus
title_full	On the type 2 poly-Bernoulli polynomials associated with umbral calculus
title_fullStr	On the type 2 poly-Bernoulli polynomials associated with umbral calculus
title_full_unstemmed	On the type 2 poly-Bernoulli polynomials associated with umbral calculus
title_sort	on the type 2 poly-bernoulli polynomials associated with umbral calculus
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/e8d9e0b6159a4953844890d2eaa01437
work_keys_str_mv	AT kimtaekyun onthetype2polybernoullipolynomialsassociatedwithumbralcalculus AT kimdaesan onthetype2polybernoullipolynomialsassociatedwithumbralcalculus AT dolgydmitryv onthetype2polybernoullipolynomialsassociatedwithumbralcalculus AT parkjinwoo onthetype2polybernoullipolynomialsassociatedwithumbralcalculus
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On the type 2 poly-Bernoulli polynomials associated with umbral calculus

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