Bell based Apostol-Bernoulli polynomials and its properties

The purpose of this paper is to construct a unified generating function involving the families of the higher-order hypergeometric Bernoulli polynomials and Lagrange–Hermite polynomials. Using the generating function and their functional equations, we investigate some properties of these polynomials. Moreover, we derive several connected formulas and relations including the Miller–Lee polynomials, the Laguerre polynomials, and the Lagrange Hermite–Miller–Lee polynomials.

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Some identities of type 2 q-Bernoulli polynomials

Journal of Inequalities and Applications ◽

10.1186/s13660-020-02413-w ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

Sang Jo Yun ◽

Jin-Woo Park

Keyword(s):

Bernoulli Polynomials

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Two-Variable Type 2 Poly-Fubini Polynomials

Mathematics ◽

10.3390/math9030281 ◽

2021 ◽

Vol 9 (3) ◽

pp. 281

Author(s):

Ghulam Muhiuddin ◽

Waseem Ahmad Khan ◽

Ugur Duran

Keyword(s):

Integral Representation ◽

Bernoulli Polynomials ◽

Stirling Numbers ◽

Higher Order ◽

Variable Type ◽

Summation Formulas

In the present work, a new extension of the two-variable Fubini polynomials is introduced by means of the polyexponential function, which is called the two-variable type 2 poly-Fubini polynomials. Then, some useful relations including the Stirling numbers of the second and the first kinds, the usual Fubini polynomials, and the higher-order Bernoulli polynomials are derived. Also, some summation formulas and an integral representation for type 2 poly-Fubini polynomials are investigated. Moreover, two-variable unipoly-Fubini polynomials are introduced utilizing the unipoly function, and diverse properties involving integral and derivative properties are attained. Furthermore, some relationships covering the two-variable unipoly-Fubini polynomials, the Stirling numbers of the second and the first kinds, and the Daehee polynomials are acquired.

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IDENTITIES OF SYMMETRY FOR GENERALIZED TWISTED BERNOULLI POLYNOMIALS TWISTED BY RAMIFIED ROOTS OF UNITY

Annals of the Alexandru Ioan Cuza University - Mathematics ◽

10.2478/aicu-2013-0006 ◽

2014 ◽

Vol 60 (1) ◽

pp. 19-36

Author(s):

Dae San Kim

Keyword(s):

Generating Function ◽

Bernoulli Polynomials ◽

Roots Of Unity ◽

Integral Expression ◽

Power Sums ◽

Exponential Generating Function

Abstract We derive eight identities of symmetry in three variables related to generalized twisted Bernoulli polynomials and generalized twisted power sums, both of which are twisted by ramified roots of unity. All of these are new, since there have been results only about identities of symmetry in two variables. The derivations of identities are based on the p-adic integral expression of the generating function for the generalized twisted Bernoulli polynomials and the quotient of p-adic integrals that can be expressed as the exponential generating function for the generalized twisted power sums.

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Some best possible integral estimates involving Bernoulli polynomials

Archiv der Mathematik ◽

10.1007/s00013-021-01640-x ◽

2021 ◽

Author(s):

Raymond Mortini ◽

Rudolf Rupp

Keyword(s):

Bernoulli Polynomials

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Some Identities of Symmetry for the Generalized Bernoulli Numbers and Polynomials

Abstract and Applied Analysis ◽

10.1155/2009/848943 ◽

2009 ◽

Vol 2009 ◽

pp. 1-8 ◽

Cited By ~ 1

Author(s):

Taekyun Kim ◽

Seog-Hoon Rim ◽

Byungje Lee

Keyword(s):

Bernoulli Polynomials ◽

Bernoulli Numbers ◽

Bernoulli Numbers And Polynomials ◽

Power Sums ◽

Invariant Integral ◽

Generalized Bernoulli Polynomials ◽

Symmetric Properties

By the properties ofp-adic invariant integral onℤp, we establish various identities concerning the generalized Bernoulli numbers and polynomials. From the symmetric properties ofp-adic invariant integral onℤp, we give some interesting relationship between the power sums and the generalized Bernoulli polynomials.

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