• 제목/요약/키워드: Genocchi numbers and polynomials

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A NOTE ON (p, q)-ANALOGUE TYPE OF FROBENIUS-GENOCCHI NUMBERS AND POLYNOMIALS

  • Khan, Waseem A.;Khan, Idrees A.
    • East Asian mathematical journal
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    • 제36권1호
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    • pp.13-24
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    • 2020
  • The main purpose of this paper is to introduce Apostol type (p, q)-Frobenius-Genocchi numbers and polynomials of order α and investigate some basic identities and properties for these polynomials and numbers including addition theorems, difference equations, derivative properties, recurrence relations. We also obtain integral representations, implicit and explicit formulas and relations for these polynomials and numbers. Furthermore, we consider some relationships for Apostol type (p, q)-Frobenius-Genocchi polynomials of order α associated with (p, q)-Apostol Bernoulli polynomials, (p, q)-Apostol Euler polynomials and (p, q)-Apostol Genocchi polynomials.

A NOTE ON THE WEIGHTED q-GENOCCHI NUMBERS AND POLYNOMIALS WITH THEIR INTERPOLATION FUNCTION

  • Arac, Serkan;Ackgoz, Mehmet;Seo, Jong-Jin
    • 호남수학학술지
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    • 제34권1호
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    • pp.11-18
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    • 2012
  • Recently, T. Kim has introduced and analysed the q-Bernoulli numbers and polynomials with weight ${\alpha}$ cf.[7]. By the same motivaton, we also give some interesting properties of the q-Genocchi numbers and polynomials with weight ${\alpha}$. Also, we derive the q-extensions of zeta type functions with weight from the Mellin transformation of this generating function which interpolates the q-Genocchi polynomials with weight at negative integers.

DEGENERATE POLYEXPONENTIAL FUNCTIONS AND POLY-EULER POLYNOMIALS

  • Kurt, Burak
    • 대한수학회논문집
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    • 제36권1호
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    • pp.19-26
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    • 2021
  • Degenerate versions of the special polynomials and numbers since they have many applications in analytic number theory, combinatorial analysis and p-adic analysis. In this paper, we define the degenerate poly-Euler numbers and polynomials arising from the modified polyexponential functions. We derive explicit relations for these numbers and polynomials. Also, we obtain some identities involving these polynomials and some other special numbers and polynomials.

A NOTE ON THE REFLECTION SYMMETRIES OF THE GENOCCHI POLYNOMIALS

  • Ryoo, Cheon-Seoung
    • Journal of applied mathematics & informatics
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    • 제27권5_6호
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    • pp.1397-1404
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    • 2009
  • It is the aim of this paper to consider the reflection symmetries of the Genocchi polynomials $G^*_n(x)$. We display the shape of Genocchi polynomials $G^*_n(x)$. Finally, we investigate the roots of the Genocchi poly-nomials $G^*_n(x)$.

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SYMMETRIC PROPERTIES OF CARLITZ'S TYPE (p, q)-GENOCCHI POLYNOMIALS

  • KIM, A HYUN
    • Journal of applied mathematics & informatics
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    • 제37권3_4호
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    • pp.317-328
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    • 2019
  • This paper defines Carlitz's type (p, q)-Genocchi polynomials and Carlitz's type (h, p, q)-Genocchi polynomials, and explains fourteen properties which can be complemented by Carlitz's type (p, q)-Genocchi polynomials and Carlitz's type (h, p, q)-Genocchi polynomials, including distribution relation, symmetric property, and property of complement. Also, it explores alternating powers sums by proving symmetric property related to Carlitz's type (p, q)-Genocchi polynomials.

HIGHER ORDER APOSTOL-TYPE POLY-GENOCCHI POLYNOMIALS WITH PARAMETERS a, b AND c

  • Corcino, Cristina B.;Corcino, Roberto B.
    • 대한수학회논문집
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    • 제36권3호
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    • pp.423-445
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    • 2021
  • In this paper, a new form of poly-Genocchi polynomials is defined by means of polylogarithm, namely, the Apostol-type poly-Genocchi polynomials of higher order with parameters a, b and c. Several properties of these polynomials are established including some recurrence relations and explicit formulas, which are used to express these higher order Apostol-type poly-Genocchi polynomials in terms of Stirling numbers of the second kind, Apostol-type Bernoulli and Frobenius polynomials of higher order. Moreover, certain differential identity is obtained that leads this new form of poly-Genocchi polynomials to be classified as Appell polynomials and, consequently, draw more properties using some theorems on Appell polynomials. Furthermore, a symmetrized generalization of this new form of poly-Genocchi polynomials that possesses a double generating function is introduced. Finally, the type 2 Apostolpoly-Genocchi polynomials with parameters a, b and c are defined using the concept of polyexponential function and several identities are derived, two of which show the connections of these polynomials with Stirling numbers of the first kind and the type 2 Apostol-type poly-Bernoulli polynomials.

A New Family of q-analogue of Genocchi Numbers and Polynomials of Higher Order

  • Araci, Serkan;Acikgoz, Mehmet;Seo, Jong Jin
    • Kyungpook Mathematical Journal
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    • 제54권1호
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    • pp.131-141
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    • 2014
  • In the present paper, we introduce the new generalization of q-Genocchi polynomials and numbers of higher order. Also, we give some interesting identities. Finally, by applying q-Mellin transformation to the generating function for q-Genocchi polynomials of higher order put we define novel q-Hurwitz-Zeta type function which is an interpolation for this polynomials at negative integers.

A NOTE ON THE ZEROS OF THE q-BERNOULLI POLYNOMIALS

  • Ryoo, Cheon-Seoung
    • Journal of applied mathematics & informatics
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    • 제28권3_4호
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    • pp.805-811
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    • 2010
  • It is the aim of this paper to observe an interesting phenomenon of 'scattering' of the zeros of the q-Bernoulli polynomials $B_{n,q}(x)$ for -1 < q < 0 in complex plane. Observe that the structure of the zeros of the Genocchi polynomials $G_n(x)$ resembles the structure of the zeros of the q-Bernoulli polynomials $B_{n,q}(x)$ as q $\rightarrow$ -1.

THE STUDY ON GENERALIZED (p, q)-POLY-GENOCCHI POLYNOMIALS WITH VARIABLE a

  • H.Y. LEE
    • Journal of Applied and Pure Mathematics
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    • 제5권3_4호
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    • pp.197-209
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    • 2023
  • In this paper, the generalized (p, q)-poly-Genocchi polynomials with variable a is defined by generalizing it more, and various properties of this polynomial are introduced. To do this, we define a generating function and use the definition to introduce some interesting properties as follows: basic properties, relation between Stirling numbers of the second kind and generalized (p, q)-poly-Genocchi polynomials with variable a and symmetric properties.