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

Khan, Waseem A.; Khan, Idrees A.; Ali, Musharraf

doi:10.24193/subbmath.2020.1.01

Cited by 7 publications

(6 citation statements)

References 9 publications

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“…The degenerate Stirling numbers of the second kind [31] are given by (see [2,[13][14][15][16][17][18][19][20][21][22][25][26][27][28][29][30][31][32])…”

Section: It Is Noticed Thatmentioning

confidence: 99%

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A New Family of Degenerate Poly-Genocchi Polynomials with Its Certain Properties

Khan

Ali

Ahmad

et al. 2021

Journal of Function Spaces

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In this paper, we introduce a new type of degenerate Genocchi polynomials and numbers, which are called degenerate poly-Genocchi polynomials and numbers, by using the degenerate polylogarithm function, and we derive several properties of these polynomials systematically. Then, we also consider the degenerate unipoly-Genocchi 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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“…The degenerate Stirling numbers of the second kind [31] are given by (see [2,[13][14][15][16][17][18][19][20][21][22][25][26][27][28][29][30][31][32])…”

Section: It Is Noticed Thatmentioning

confidence: 99%

“…The classical Euler polynomials E n ðxÞ and the classical Genocchi polynomials G n ðxÞ are, respectively, defined by the following generating functions (see [12][13][14][15][16][17][18][19][20][21][22]):…”

Section: Introductionmentioning

confidence: 99%

A New Family of Degenerate Poly-Genocchi Polynomials with Its Certain Properties

Khan

Ali

Ahmad

et al. 2021

Journal of Function Spaces

Self Cite

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show abstract

“…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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“…The classical Genocchi numbers G n , the classical Genocchi polynomials G n (x) and the generalized Genocchi polynomials G (α) n (x) of (real or complex) order α are usually defined by means of the following generating functions (see [11,12,[15][16][17][18][19][20][21][22][23][24]):…”

Section: Introductionmentioning

confidence: 99%