Symmetric identities of Hermite-Bernoulli polynomials and Hermite-Bernoulli numbers attached to a dirichlet character χ

Serkan Araci; Waseem Ahmad Khan; Kottakkaran Sooppy Nisar

doi:10.3390/sym10120675

Symmetric identities of Hermite-Bernoulli polynomials and Hermite-Bernoulli numbers attached to a dirichlet character χ

Serkan Araci
, Waseem Ahmad Khan
, Kottakkaran Sooppy Nisar

Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We aim to introduce arbitrary complex order Hermite-Bernoulli polynomials and Hermite-Bernoulli numbers attached to a Dirichlet character χ and investigate certain symmetric identities involving the polynomials, by mainly using the theory of p-adic integral on ℤ_p. The results presented here, being very general, are shown to reduce to yield symmetric identities for many relatively simple polynomials and numbers and some corresponding known symmetric identities.

Original language	English
Article number	675
Journal	Symmetry
Volume	10
Issue number	12
DOIs	https://doi.org/10.3390/sym10120675
State	Published - 1 Dec 2018

Keywords

Bernoulli numbers and polynomials
Generalized bernoulli polynomials and numbers attached to a Dirichlet character χ
Generalized bernoulli polynomials and numbers of arbitrary complex order
Q-Volkenborn integral on ℤ

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10.3390/sym10120675

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title = "Symmetric identities of Hermite-Bernoulli polynomials and Hermite-Bernoulli numbers attached to a dirichlet character χ",

abstract = "We aim to introduce arbitrary complex order Hermite-Bernoulli polynomials and Hermite-Bernoulli numbers attached to a Dirichlet character χ and investigate certain symmetric identities involving the polynomials, by mainly using the theory of p-adic integral on ℤp. The results presented here, being very general, are shown to reduce to yield symmetric identities for many relatively simple polynomials and numbers and some corresponding known symmetric identities.",

keywords = "Bernoulli numbers and polynomials, Generalized bernoulli polynomials and numbers attached to a Dirichlet character χ, Generalized bernoulli polynomials and numbers of arbitrary complex order, Q-Volkenborn integral on ℤ",

author = "Serkan Araci and Khan, \{Waseem Ahmad\} and Nisar, \{Kottakkaran Sooppy\}",

note = "Publisher Copyright: {\textcopyright} 2018 by the authors.",

year = "2018",

month = dec,

day = "1",

doi = "10.3390/sym10120675",

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volume = "10",

journal = "Symmetry",

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T1 - Symmetric identities of Hermite-Bernoulli polynomials and Hermite-Bernoulli numbers attached to a dirichlet character χ

AU - Araci, Serkan

AU - Khan, Waseem Ahmad

AU - Nisar, Kottakkaran Sooppy

PY - 2018/12/1

Y1 - 2018/12/1

N2 - We aim to introduce arbitrary complex order Hermite-Bernoulli polynomials and Hermite-Bernoulli numbers attached to a Dirichlet character χ and investigate certain symmetric identities involving the polynomials, by mainly using the theory of p-adic integral on ℤp. The results presented here, being very general, are shown to reduce to yield symmetric identities for many relatively simple polynomials and numbers and some corresponding known symmetric identities.

AB - We aim to introduce arbitrary complex order Hermite-Bernoulli polynomials and Hermite-Bernoulli numbers attached to a Dirichlet character χ and investigate certain symmetric identities involving the polynomials, by mainly using the theory of p-adic integral on ℤp. The results presented here, being very general, are shown to reduce to yield symmetric identities for many relatively simple polynomials and numbers and some corresponding known symmetric identities.

KW - Bernoulli numbers and polynomials

KW - Generalized bernoulli polynomials and numbers attached to a Dirichlet character χ

KW - Generalized bernoulli polynomials and numbers of arbitrary complex order

KW - Q-Volkenborn integral on ℤ

UR - https://www.scopus.com/pages/publications/85058981889

U2 - 10.3390/sym10120675

DO - 10.3390/sym10120675

M3 - Article

AN - SCOPUS:85058981889

SN - 2073-8994

VL - 10

JO - Symmetry

JF - Symmetry

IS - 12

M1 - 675

ER -

Symmetric identities of Hermite-Bernoulli polynomials and Hermite-Bernoulli numbers attached to a dirichlet character χ

Abstract

Keywords

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