A class of Frobenius-type Eulerian polynomials

Boutiche, Mohamed Amine; Rahmani, Mourad

doi:10.1216/rmj-2018-48-3-1003

Cited by 11 publications

(13 citation statements)

References 20 publications

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“…respectively. Moreover, the Apostol type (p, q)-Frobenius-Euler polynomials were introduced in [10] and some new identities satisfied by the Apostol type (p, q)-Frobenius-Euler polynomials were obtained in [10] (see also the recent works [7], [22] and [21]).…”

Section: Introduction Definitions and Preliminariesmentioning

confidence: 99%

A class of big (p,q)-Appell polynomials and their associated difference equations

Srivástava

Yaşar

Özarslan

2019

Filomat

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In the present paper, we introduce and investigate the big (p, q)-Appell polynomials. We prove an equivalance theorem satisfied by the big (p, q)-Appell polynomials. As a special case of the big (p, q)-Appell polynomials, we present the corresponding equivalence theorem, recurrence relation and difference equation for the big q-Appell polynomials. We also present the equivalence theorem, recurrence relation and differential equation for the usual Appell polynomials. Moreover, for the big (p, q)-Bernoulli polynomials and the big (p, q)-Euler polynomials, we obtain recurrence relations and difference equations. In the special case when p = 1, we obtain recurrence relations and difference equations which are satisfied by the big q-Bernoulli polynomials and the big q-Euler polynomials. In the case when p = 1 and q → 1−, the big (p, q)-Appell polynomials reduce to the usual Appell polynomials. Therefore, the recurrence relation and the difference equation obtained for the big (p, q)-Appell polynomials coincide with the recurrence relation and differential equation satisfied by the usual Appell polynomials. In the last section, we have chosen to also point out some obvious connections between the (p, q)-analysis and the classical q-analysis, which would show rather clearly that, in most cases, the transition from a known q-result to the corresponding (p, q)-result is fairly straightforward.

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Section: Introduction Definitions and Preliminariesmentioning

confidence: 99%

A class of big (p,q)-Appell polynomials and their associated difference equations

Srivástava

Yaşar

Özarslan

2019

Filomat

Self Cite

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“…Special polynomials including the reputed Bernoulli, Hermite and Euler polynomials and also their generalizations with many applications have been investigated extensively and studied by many mathematicians and also physicists, cf. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. For instance, Carlitz [2,3] introduced and investigated the Eulerian polynomials and higher order Eulerian polynomials, which are closely related with the Euler and Bernoulli numbers and polynomials.…”

Section: Introductionmentioning

confidence: 99%

“…The Frobenius type Eulerian polynomials A ( ) n (x; ) of order 2 C are de…ned by means of the following exponential generating function as follows (see [2,3,7,8,9,18]):…”

Section: Introductionmentioning

confidence: 99%

A Novel Kind of Hermite Based Frobenius Type Eulerian Polynomials

Khan¹,

Nisar²,

Açıkgöz³

et al. 2019

Preprint

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We introduce a new kind of extended Hermite-based Frobenius type Eulerian polynomials and then derive diverse explicit and implicit summation equations including some symmetric formulas by utilizing series manupulation method. Multifarious summation formulas and identities given earlier for some well known polynomials such as Eulerian polynomials and Frobenius type Eulerian polynomials are generalized.

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“…One of the most popular studies in q-calculus is the qextension of the some special polynomials such as Bernoulli, Eulerian, Genocchi, Euler polynomials, cf. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] and see also the references cited therein. The classical Eulerian polynomials are …rstly considered by Leonhard Euler in his Remarques sur un beau rapport entre les séries des puissances tant directes que réciproques in 1749 (…rst printed in 1765) inwhich he de…nes a method of computing values of the zeta function at negative integers.…”

Section: Introductionmentioning

confidence: 99%

“…[3,4,6,7]. Moreover, the Frobenius-type Eulerian polynomials are introduced and studied in [19]. In this paper, we perform to give a novel class of q-generalization of the Hermite based Frobenius type Eulerian polynomials and to derive multifarious correlation, implicit summation formula, identities, explicit formulas and recurrence relations for the mentioned polynomials by means of the series manipulation methods.…”

Section: Introductionmentioning

confidence: 99%

Multifarious Results for q-Hermite Based Frobenius Type Eulerian Polynomials

Khan¹,

Khan²,

Açıkgöz³

et al. 2019

Preprint

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In this paper, a new class of q-Hermite based Frobenius type Eulerian polynomials is introduced by means of generating function and series representation. Several fundamental formulas and recurrence relations for these polynomials are derived via different generating methods. Furthermore, diverse correlations including the q-Apostol-Bernoulli polynomials, the q-Apostol-Euler poynoomials, the q-Apostol-Genocchi polynomials and the q-Stirling numbers of the second kind are also established by means of the their generating functions.

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A class of Frobenius-type Eulerian polynomials

Cited by 11 publications

References 20 publications

A class of big (p,q)-Appell polynomials and their associated difference equations

A class of big (p,q)-Appell polynomials and their associated difference equations

A Novel Kind of Hermite Based Frobenius Type Eulerian Polynomials

Multifarious Results for q-Hermite Based Frobenius Type Eulerian Polynomials

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