SOME IDENTITIES ON THE BERNSTEIN AND q-GENOCCHI POLYNOMIALS

Kim, Hyun-Mee

doi:10.4134/bkms.2013.50.4.1289

Cited by 2 publications

(4 citation statements)

References 26 publications

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“…where the notation of I −1 (f ) is called the fermionic p-adic integral on Z p (see [3], [5], [6], [7], [8], [9], [10], [11], [14], [23], [29], [30], [31], [32], [33], [35], [36], [38], [39], [40], [41]).…”

Section: Preliminariesmentioning

confidence: 99%

Identities involving the $\left(h,q\right)$-Genocchi polynomials and $\left(h,q\right)$-Zeta-type function

Bagdasaryan,

Sen,

et al. 2013

Preprint

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The fundamental objective of this paper is to obtain some interesting properties for (h, q)-Genocchi numbers and polynomials by using the fermionic p-adic q-integral on Zp and mentioned in the paper q-Bernstein polynomials. By considering the q-Euler zeta function defined by T. Kim, which can also be obtained by applying the Mellin transformation to the generating function of (h, q)-Genocchi polynomials, we study (h, q)-Zeta-type function. We derive symmetric properties of (h, q)-Zeta function and from these properties we give symmetric property of (h, q)-Genocchi polynomials.

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Section: Preliminariesmentioning

confidence: 99%

Identities involving the $\left(h,q\right)$-Genocchi polynomials and $\left(h,q\right)$-Zeta-type function

Bagdasaryan,

Sen,

et al. 2013

Preprint

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“…e group of straight di erential conditions emerging from the creating capacity of Catalan-Daehee numbers was thought of as in [3]. In [4], a few properties and personalities related with Catalan numbers and polynomials were inferred by using umbral analytic procedures. Dolgy et al [5] gave a few new characters for those numbers and polynomials got from p-adic Volkenborn vital on Z p .…”

Section: Introductionmentioning

confidence: 99%

“…Let f be a uniformly differentiable function on Z p . en, the p-adic q-integral on Z p is defined by Kim as [4,7] 􏽚…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Note on q‐Analogues of Degenerate Catalan‐Daehee Numbers and Polynomials

Khan

2022

Journal of Mathematics

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Recently, Yuankui et al. (Filomat J. 35 (5):17, 2022) studied q -analogues of Catalan-Daehee numbers and polynomials by making use of p -adic q -integrals on ℤ p . Motivated by this study, we consider q -analogues of degenerate Catalan-Daehee numbers and polynomials with the help of p -adic q -integrals on ℤ p . By using their generating function, we derive some new relations including the degenerate Stirling numbers of the first and second kinds. Moreover, we also derive some new identities and properties of this type of polynomials and numbers.

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SOME IDENTITIES ON THE BERNSTEIN AND q-GENOCCHI POLYNOMIALS

Cited by 2 publications

References 26 publications

Identities involving the $\left(h,q\right)$-Genocchi polynomials and $\left(h,q\right)$-Zeta-type function

Identities involving the $\left(h,q\right)$-Genocchi polynomials and $\left(h,q\right)$-Zeta-type function

A Note on q‐Analogues of Degenerate Catalan‐Daehee Numbers and Polynomials

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