On a new family related to truncated exponential and Sheffer polynomials

Khan, Subuhi; Yasmin, Ghazala; Ahmad, Naeem

doi:10.1016/j.jmaa.2014.04.028

Cited by 15 publications

(14 citation statements)

References 11 publications

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“…n (x, y), For example, we have e (2) n (x, y) = [2]e n (x, y) e (1) n (x, 1) = [r]e n (x) e (2) n (x, 1) = [2]e n (x) and e (1) n (x, 1) = e n (x). (17) As it is shown in [6,7], the 2VTEP e (r)…”

Section: Introductionmentioning

confidence: 88%

“…For the case y = 1, the polynomials [2] e n (x, 1) reduce to the truncated-exponential polynomials [2] e n (x). Therefore, by taking y = 1 in Equation (59), we get the following generating function for the truncated-exponential Apostol-type polynomials (TEATP) [2] n (x, y) [6]. Again for α = 1, we get the corresponding results for the 2-variable truncated-exponential Bernoulli polynomials (2VTEBP) e (r) B n (x, y), 2-variable truncated-exponential Euler polynomials (2VTEEP) e (r) E n (x, y) and 2-variable truncated-exponential Genocchi polynomials (2VTEGP) e (r) G n (x, y).…”

Section: Remarkmentioning

confidence: 99%

“…Actually, Dattoli et al [4] systematically studied the properties of these polynomials. The definition (6) does lead us to most (if not all) of the properties of the polynomials e n (x). We note the following representation: e n (x) = 1 n!…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Introductionmentioning

confidence: 88%

Section: Remarkmentioning

confidence: 99%

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

et al. 2019

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“…Proof. We recall the following recurrence relations for the truncated-Sheffer polynomials e (r) s n+1 (x, y) from [19]:…”

Section: Theoremmentioning

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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“…is irreducible in Q[x]. For further properties and applications of these polynomials, see, for example, [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38].…”

Section: Introductionmentioning

confidence: 99%

Truncated-Exponential-Based Appell-Type Changhee Polynomials

2020

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The truncated exponential polynomials em(x) (1), their extensions, and certain newly-introduced polynomials which combine the truncated exponential polynomials with other known polynomials have been investigated and applied in various ways. In this paper, by incorporating the Appell-type Changhee polynomials Chn*(x) (10) and the truncated exponential polynomials in a natural way, we aim to introduce so-called truncated-exponential-based Appell-type Changhee polynomials eCn*(x) in Definition 1. Then, we investigate certain properties and identities for these new polynomials such as explicit representation, addition formulas, recurrence relations, differential and integral formulas, and some related inequalities. We also present some integral inequalities involving these polynomials eCn*(x). Further we discuss zero distributions of these polynomials by observing their graphs drawn by Mathematica. Lastly some open questions are suggested.

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On a new family related to truncated exponential and Sheffer polynomials

Cited by 15 publications

References 11 publications

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

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

Finding Determinant Forms of Certain Hybrid Sheffer Sequences

Truncated-Exponential-Based Appell-Type Changhee Polynomials

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