Determinantal approach to certain mixed special polynomials related to Gould–Hopper polynomials

Khan, Subuhi; Riyasat, Mumtaz

doi:10.1016/j.amc.2014.11.081

Cited by 13 publications

(9 citation statements)

References 10 publications

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“…Then, in view of Remark 4, the assertions of the theorems in this section can be verified by the corresponding theorems in ( [5], pp. [17][18][19][20][21][22][23][24]. In this regard, proofs are omitted.…”

Section: Sheffer Sequencesmentioning

confidence: 99%

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Legendre-Gould Hopper-Based Sheffer Polynomials and Operational Methods

et al. 2020

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A remarkably large of number of polynomials have been presented and studied. Among several important polynomials, Legendre polynomials, Gould-Hopper polynomials, and Sheffer polynomials have been intensively investigated. In this paper, we aim to incorporate the above-referred three polynomials to introduce the Legendre-Gould Hopper-based Sheffer polynomials by modifying the classical generating function of the Sheffer polynomials. In addition, we investigate diverse properties and formulas for these newly introduced polynomials.

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Section: Sheffer Sequencesmentioning

confidence: 99%

“…For more details and applications of operational methods and quasi-monomials, one may be referred, for example, to [1][2][3]5,[9][10][11][12][13][14][15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Legendre-Gould Hopper-Based Sheffer Polynomials and Operational Methods

et al. 2020

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“…A vast literature associated with the matrix and other approaches to several special polynomials and corresponding hybrid forms can be found, see [8][9][10][11][12][13][14][15][16][17]. These matrix forms helps in solving various algorithms and in finding the solution of numerical and a general linear interpolation problems.…”

Section: Introductionmentioning

confidence: 99%

Finding Determinant Forms of Certain Hybrid Sheffer Sequences

et al. 2019

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In this article, the integral transform is used to introduce a new family of extended hybrid Sheffer sequences via generating functions and operational rules. The determinant forms and other properties of these sequences are established using a matrix approach. The correspondingresults for the extended hybrid Appell sequences are also obtained. Certain examples in terms of the members of the extended hybrid Sheffer and Appell sequences are framed. By employing operational rules, the identities involving the Lah, Stirling and Pascal matrices are derived for the aforementioned sequences.

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“…For b = c = e, a = 1, Remarks 2.3-2.5 give the Gould-Hopper-Apostol-Bernoulli, Euler and Genocchi polynomials, each of order α, which for λ = 1 yield Gould-Hopper-Bernoulli, Euler and Genocchi polynomials, each of order α, which again for α = 1 yield Gould-Hopper-Bernoulli, Euler and Genocchi polynomials[17,19]. Note For j = 2, Remarks 2.3-2.5 give the generalized-Hermite-Apostol-Bernoulli, Euler and Genocchi polynomials, each of order α, which for b = c = e, a = 1 yield Hermite-Apostol-Bernoulli, Euler and Genocchi polynomials, each of order α, which again for λ = 1 yield Hermite-Bernoulli, Euler and Genocchi polynomials, each of order α, which further for α = 1 reduce to Hermite-Bernoulli, Euler and Genocchi polynomials.…”

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confidence: 99%

Some unified formulas involving generalized-Apostol-type-Gould-Hopper polynomials and multiple power sums

Aracı¹,

Riyasat²,

Khan³

et al. 2019

J. Math. Computer Sci.

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The article aims to introduce a new unified class of generalized Apostol type polynomials. Further, under a slight modification on the parameters associated to the generalized Apostol type and generalized Gould-Hopper polynomials and by the use of generating method, we introduce a new class of generalized-Apostol-type-Gould-Hopper polynomials. We state some quasi-monomial properties for a new class of extensions of generalized Apostol type polynomials as well as, some summation, multiplication and explicit formulae which connect this polynomial class with the λ-Stirling numbers of second kind and generalized Hurwitz zeta function. Some general symmetry identities involving multiple power sums are also established. The new class of polynomials contains as its special cases, not only the generalized-Gould-Hopper-Apostol-Bernoulli, Euler and Genocchi polynomials but many more known smaller classes of polynomials. Finally, the these polynomials are framed within the context of generalized modified Milne-Thomson's polynomials.

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Determinantal approach to certain mixed special polynomials related to Gould–Hopper polynomials

Cited by 13 publications

References 10 publications

Legendre-Gould Hopper-Based Sheffer Polynomials and Operational Methods

Legendre-Gould Hopper-Based Sheffer Polynomials and Operational Methods

Finding Determinant Forms of Certain Hybrid Sheffer Sequences

Some unified formulas involving generalized-Apostol-type-Gould-Hopper polynomials and multiple power sums

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