A new generalization of Apostol-type Laguerre–Genocchi polynomials

Khan, Nabiullah; Usman, Talha; Choi, Junesang

doi:10.1016/j.crma.2017.04.010

Cited by 19 publications

(18 citation statements)

References 16 publications

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“…n (x, y) (see [29]). In this regard, the results presented here can be specialized to yield or be closely connected with some known identities and formulas (see, e.g., [5,13,[18][19][20][21][22][23][24][27][28][29]40,41], and the references cited therein). Therefore, the results presented in this article seem to be potentially useful in arising problems of the aforementioned fields.…”

Section: Discussionmentioning

confidence: 99%

A new class of generalized polynomials associated with Laguerre and Bernoulli polynomials

Khan¹,

Usman²,

Choi³

2019

Turk J Math

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Motivated by their importance and potential for applications in certain problems in number theory, combinatorics, classical and numerical analysis, and other fields of applied mathematics, a variety of polynomials and numbers with their variants and extensions have recently been introduced and investigated. In this paper, we aim to introduce generalized Laguerre-Bernoulli polynomials and investigate some of their properties such as explicit summation formulas, addition formulas, implicit formulas, and symmetry identities. Relevant connections of the results presented here with those relatively simple numbers and polynomials are considered.

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Section: Discussionmentioning

confidence: 99%

A new class of generalized polynomials associated with Laguerre and Bernoulli polynomials

Khan¹,

Usman²,

Choi³

2019

Turk J Math

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“…For m ∈ N, a relation between these functions and the Apostol-Bernoulli numbers is given by (cf. [1]): (14) Φ(λ, −m, a) = − B m+1 (a; λ) m + 1 .…”

Section: Apostol-type Numbers and Polynomials With Their Interpolatiomentioning

confidence: 99%

Identities for Dirichlet and Lambert-type series arising from the numbers of a certain special word

Kucukoglu

Şimşek

2019

APPL ANAL DISCRETE M

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The goal of this paper is to give several new Dirichlet-type series associated with the Riemann zeta function, the polylogarithm function, and also the numbers of necklaces and Lyndon words. By applying Dirichlet convolution formula to number-theoretic functions related to these series, various novel identities and relations are derived. Moreover, some new formulas related to Bernoulli-type numbers and polynomials obtain from generating functions and these Dirichlet-type series. Finally, several relations among the Fourier expansion of Eisenstein series, the Lambert series and the number-theoretic functions are given.

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“…where B n are the nth Bernoulli numbers (see References [11][12][13][14]; see also Reference [15] (Section 1.7)). From Equation 2and 3, one gets…”

Section: Introductionmentioning

confidence: 99%

Symmetric Identities of Hermite-Bernoulli Polynomials and Hermite-Bernoulli Numbers Attached to a Dirichlet Character χ

2018

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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.

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A new generalization of Apostol-type Laguerre–Genocchi polynomials

Cited by 19 publications

References 16 publications

A new class of generalized polynomials associated with Laguerre and Bernoulli polynomials

A new class of generalized polynomials associated with Laguerre and Bernoulli polynomials

Identities for Dirichlet and Lambert-type series arising from the numbers of a certain special word

Symmetric Identities of Hermite-Bernoulli Polynomials and Hermite-Bernoulli Numbers Attached to a Dirichlet Character χ

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