Some identities of degenerate Euler polynomials associated with degenerate Bernstein polynomials

Kim, Won Joo; Ким, Дае Сан; Kim, Han Young; Kim, Taekyun

doi:10.1186/s13660-019-2110-y

Cited by 6 publications

(4 citation statements)

References 11 publications

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“…In the theory of special functions and special polynomials, the degenerate forms for polynomials and functions have been worked and developed by several mathematicians cf. [5,6,8,9,10,[12][13][14][15][16][17][18][19][20][21][22][23] and see also the references cited therein. For example, Carlitz [12] considered the degenerate Euler polynomials of higher order and presented diverse properties.…”

Section: Motivationmentioning

confidence: 99%

“…x e t λ for a real number λ is given by (cf. [5,6,8,9,10,[12][13][14][15][16][17][18][19][20][21][22][23]):…”

mentioning

confidence: 99%

“…As the parameters , λ β and γ goes to 0 , the generalized degenerate Gould-Hopper based fully degenerate Bernoulli, Euler and Genocchi polynomials reduce to the usual Bernoulli, Euler and Genocchi polynomials, cf [12,15,21,23,24,26,27,29,30,33,34]…”

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confidence: 99%

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Generalized Gould-Hopper Based Fully Degenerate Central Bell Polynomials

Duran¹,

Açıkgöz²

2020

TJANT

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In this paper, we first provide the generalized degenerate Gould-Hopper polynomials via the degenerate exponential functions and then give various relations and formulas such as addition formula and explicit identity. Moreover, we consider the generalized Gould-Hopper based degenerate central factorial numbers of the second kind and present several identities and relationships. Furthermore, we introduce the generalized Gould-Hopper based fully degenerate central Bell polynomials and investigated multifarious correlations and formulas including summation formulas, derivation rule and correlations with the Stirling numbers of the first kind, the generalized Gould-Hopper based degenerate central factorial numbers of the second kind and the generalized degenerate Gould-Hopper polynomials. We then acquire some relations with the degenerate Bernstein polynomials for the generalized Gould-Hopper based fully degenerate central Bell polynomials. Finally, we consider the Gould-Hopper based fully degenerate Bernoulli, Euler and Genocchi polynomials and by utilizing these polynomials, we develop some representations for the generalized Gould-Hopper based fully degenerate central Bell polynomials.

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Section: Motivationmentioning

confidence: 99%

“…x e t λ for a real number λ is given by (cf. [5,6,8,9,10,[12][13][14][15][16][17][18][19][20][21][22][23]):…”

mentioning

confidence: 99%

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Generalized Gould-Hopper Based Fully Degenerate Central Bell Polynomials

Duran¹,

Açıkgöz²

2020

TJANT

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“…where B n,k (x 1 , x 2 |λ) are called two variable degenerate Bernstein polynomials of degree n as followings (see, [2][3][4][5][6]9,[14][15][16][17][18][19][20][21][22][23][24][25][26][27]):…”

Section: Theoremmentioning

confidence: 99%