A New Class of Laguerre-Based Poly-Euler and Multi Poly-Euler Polynomials

Khan, Nabiullah; Usman, Talha

doi:10.18576/jant/040205

Cited by 18 publications

(21 citation statements)

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“…These results extend some known summations and identities of generalized Hermite multipoly-Bernoulli numbers and polynomials of the second kind studied by Qi et al [11], Dattoli et al [5], Khan [7] and Pathan and Khan [9,10].…”

Section: It Is Easily Seen From Definition (1) Thatsupporting

confidence: 86%

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Multiple-Poly-Bernoulli Polynomials of the Second Kind Associated with Hermite Polynomials

Khan

Ghayasuddin

Shadab

2017

Fasciculi Mathematici

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Abstract. In this paper, we introduce a new class of Hermite multiple-poly-Bernoulli numbers and polynomials of the second kind and investigate some properties for these polynomials. We derive some implicit summation formulae and general symmetry identities by using different analytical means and applying generating functions. The results derived here are a generalization of some known summation formulae earlier studied by Pathan and Khan.Key words: Hermite polynomials, multi-poly-Bernoulli polynomials of the second kind, Hermite multi-poly-Bernoulli polynomials of the second kind, summation formulae, symmetric identities.

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Section: It Is Easily Seen From Definition (1) Thatsupporting

confidence: 86%

“…n (x) are called the higher order Bernoulli polynomials of the first kind given by the generating function (see [7,8,9,10]):…”

Section: It Is Easily Seen From Definition (1) Thatmentioning

confidence: 99%

Multiple-Poly-Bernoulli Polynomials of the Second Kind Associated with Hermite Polynomials

Khan

Ghayasuddin

Shadab

2017

Fasciculi Mathematici

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“…In this section, we establish symmetry identities for the q-degenerate poly-Bernoulli polynomials β (k) n,q (x; λ) and the degenerate Hermite poly-Bernoulli polynomials with q-parameter H β (k) n,q (x, y; λ) by applying the generating function(2.1) and (2.2). The results extend some known identities of Khan [13], [14], [15], [16], Pathan and Khan [19], [20], [21], [22]. Theorem 4.1.…”

Section: General Symmetry Identitiessupporting

confidence: 78%

Degenerate Hermite poly-Bernoulli numbers and polynomials with q-parameter

Khan

Ali³

2020

Stud. Univ. Babes-Bolyai Math.

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In this paper, we introduce a new class of degenerate Hermite poly-Bernoulli polynomials with q-parameter and give some identities of these polynomials related to the Stirling numbers of the second kind. Some implicit summation formulae and general symmetry identities are derived by using different analytical means and applying generating functions. These results extend some known summations and identities of degenerate Hermite poly-Bernoulli numbers and polynomials.Mathematics Subject Classification (2010): 11B68, 11B73, 11B75, 33C45.

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“…Numerous mathematicians including Kim and Ryoo [1], Kim and Kim [2], Kim et al [3][4][5], Khan [6,7] have concentrated their study on polynomials and its combination with Bernoulli, Genocchi, Euler, and tangent numbers. One of the essential classes of these sequences is the class of Appell polynomials.…”

Section: Introductionmentioning

confidence: 99%