Some implicit summation formulas and symmetric identities for the generalized Hermite-Based polynomials

Pathan, M. A.; Khan, Waseem A.

doi:10.17114/j.aua.2014.39.11

Cited by 17 publications

(31 citation statements)

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“…Such type of works, introduced here by the approach given in the recent works of Khan [5] and Pathan and Khan [13,14,15]. …”

Section: General Symmetry Identitiesmentioning

confidence: 99%

Some New Classes of Generalized Lagrange-Based Apostol Type Hermite Polynomials

Khan¹,

Nisar²

2018

Preprint

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Abstract. In this paper, we introduce a general family of Lagrange-based Apostoltype Hermite polynomials thereby unifying the Lagrange-based Apostol HermiteBernoulli and the Lagrange-based Apostol Hermite-Genocchi polynomials. We also define Lagrange-based Apostol Hermite-Euler polynomials via the generating function. In terms of these generalizations, we find new and useful relations between the unified family and the Apostol Hermite-Euler polynomials. We also derive their explicit representations and list some basic properties of each of them. Some implicit summation formulae and general symmetry identities are derived by using different analytical means and applying generating functions.

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“…Such type of works, introduced here by the approach given in the recent works of Khan [5] and Pathan and Khan [13,14,15]. …”

Section: General Symmetry Identitiesmentioning

confidence: 99%

Some New Classes of Generalized Lagrange-Based Apostol Type Hermite Polynomials

Khan¹,

Nisar²

2018

Preprint

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“…The classical Bernoulli polynomials B n (x), the classical Euler polynomials E n (x), and the classical Genocchi polynomials G n (x) each of degree n are defined respectively by the following generating functions (see [3][4][5][6][7][8][9][10][11][12][13][14][15][16] G n (x) t n n! (|t| < π) .…”

Section: Introductionmentioning

confidence: 99%

“…For obtaining implicit summation formula and general symmetry identities, we use the proof techniques of Dattoli et al [3], and Pathan and Khan [13].…”

Section: Introductionmentioning

confidence: 99%

A new class of partially degenerate Hermite-Genocchi polynomials

Khan¹,

Aracı²,

Açıkgöz³

et al. 2017

J. Nonlinear Sci. Appl.

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In this paper, firstly we introduce not only partially degenerate Hermite-Genocchi polynomials, but also a new generalization of degenerate Hermite-Genocchi polynomials. Secondly, we investigate some behaviors of these polynomials. Furthermore, we establish some implicit summation formulae and symmetry identities by making use of the generating function of partially degenerate Hermite-Genocchi polynomials. Finally, some results obtained here extend well-known summations and identities which we stated in the paper.

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“…In this section, we employ the definition of the 2-variable truncated-exponential-based Apostol-type polynomials e (r) Y (α) n,β (x, y; k, a, b) that help in proving the generalizations of the previous works of Khan et al [33] and Pathan and Khan (see [34][35][36]). For the derivation of implicit formulas involving the 2-variable truncated-exponential-based Apostol-type polynomials e (r) Y (α) n,β (x, y; k, a, b), the same considerations as developed for the ordinary Hermite and related polynomials in the works by Khan et al [33] and Pathan et al (see [34][35][36]) apply as well. We first prove the following results involving the 2-variable truncated-exponential-based Apostol-type polynomials e (r) Y (α) n,β (x, y; k, a, b).…”

Section: Implicit Formulas Involving the 2-variable Truncated-exponenmentioning

confidence: 99%

A Note on the Truncated-Exponential Based Apostol-Type Polynomials

et al. 2019

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In this paper, we propose to investigate the truncated-exponential-based Apostol-type polynomials and derive their various properties. In particular, we establish the operational correspondence between this new family of polynomials and the familiar Apostol-type polynomials. We also obtain some implicit summation formulas and symmetric identities by using their generating functions. The results, which we have derived here, provide generalizations of the corresponding known formulas including identities involving generalized Hermite-Bernoulli polynomials.

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Some implicit summation formulas and symmetric identities for the generalized Hermite-Based polynomials

Cited by 17 publications

References 0 publications

Some New Classes of Generalized Lagrange-Based Apostol Type Hermite Polynomials

Some New Classes of Generalized Lagrange-Based Apostol Type Hermite Polynomials

A new class of partially degenerate Hermite-Genocchi polynomials

A Note on the Truncated-Exponential Based Apostol-Type Polynomials

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