A Note on Parametric Kinds of the Degenerate Poly-Bernoulli and Poly-Genocchi Polynomials

Kim, Taekyun; Khan, Waseem A.; Sharma, Sunil Kumar; Ghayasuddin, Mohd

doi:10.3390/sym12040614

Cited by 19 publications

(17 citation statements)

References 17 publications

(11 reference statements)

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“…standing for the Stirling numbers of the second kind given by means of the following generating function: [14,15,18,[20][21][22][23][24][25][26][27][28][29][30][31][32]).…”

Section: Note Thatmentioning

confidence: 99%

Degenerate polyexponential-Genocchi numbers and polynomials

Khan¹,

Khan²,

Khan³

2020

J. Math. Computer Sci.

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Recently, Kim et al. in [T. Kim, D. S. Kim, H. Y. Kim, L.-C. Jang, Informatica, 3 (2020), 8 pages] studied the degenerate poly-Bernoulli numbers and polynomials which are defined by using the polylogarithm function. In this paper, we study the degenerate polyexponential-Genocchi polynomials and numbers arising from polyexponential function and derive their explicit expressions and some identity involving them. In the final section, we introduce degenerate unipoly-Genocchi polynomials attached to an arithmetic function, by using polylogarithm function and investigate some identities for those polynomials.

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“…standing for the Stirling numbers of the second kind given by means of the following generating function: [14,15,18,[20][21][22][23][24][25][26][27][28][29][30][31][32]).…”

Section: Note Thatmentioning

confidence: 99%

Degenerate polyexponential-Genocchi numbers and polynomials

Khan¹,

Khan²,

Khan³

2020

J. Math. Computer Sci.

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“…In the inverse expression to (1.13), the Stirling numbers of the second kind are defined by [10,12,13]).…”

Section: Introductionmentioning

confidence: 99%

A Novel Kind of the Type 2 Poly-Fubini Polynomials and Numbers

Khan¹

2020

Preprint

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Motivation by the definition of the type 2 poly-Bernoulli polynomials introduced by Kim-Kim [9], in the present paper, we consider a new class of new generating function for the Fubini polynomials, called the type 2 poly-Fubini polynomials by means of the polyexponential function. Then, we derive some useful relations and properties. We show that the type 2 poly-Fubini polynomials equal a linear combination of the classical of the Fubini polynomials and Stirling numbers of the first kind. In a special case, we give a relation between the type 2 poly-Fubini polynomials and Bernoulli polynomials of order r. Moreover, inspired by the definition of the unipoly-Bernoulli polynomials introduced by Kim-Kim [9]. We introduce the type 2 unipoly-Fubini polynomials by means of unipoly function and give multifarious properties including derivative and integral properties. Furthermore, we provide a correlation between the unipoly-Fubini polynomials and the classical Fubini polynomials.

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“…Carlitz's [2,3] initiated a study of degenerate versions of some special polynomials and numbers, namely the degenerate Bernoulli and Euler polynomials and numbers. Kim and Kim et al [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] have studied the degenerate versions of special numbers and polynomials actively. This idea provides a powerful tool to define special numbers and polynomials of their degenerate versions.…”

Section: Introductionmentioning

confidence: 99%

On A New Type of Degenerate Poly-Fubini Numbers and Polynomials

Khan¹

2020

Preprint

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In this paper, we introduce a new type of degenerate poly-Fubini polynomials and numbers, are called degenerate poly-Fubini polynomials and numbers, by using the degenerate polylogarithm function and derive several properties on the degenerate poly-Fubini polynomials and numbers. In the last section, we also consider the degenerate unipoly-Fubini polynomials attached to an arithmetic function, by using the degenerate polylogarithm function and investigate some identities of those polynomials. In particular, we give some new explicit expressions and identities of degenerate unipoly polynomials related to special numbers and polynomials.

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A Note on Parametric Kinds of the Degenerate Poly-Bernoulli and Poly-Genocchi Polynomials

Cited by 19 publications

References 17 publications

Degenerate polyexponential-Genocchi numbers and polynomials

Degenerate polyexponential-Genocchi numbers and polynomials

A Novel Kind of the Type 2 Poly-Fubini Polynomials and Numbers

On A New Type of Degenerate Poly-Fubini Numbers and Polynomials

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