• 제목/요약/키워드: Genocchi numbers and polynomials

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REFLECTION SYMMETRIES OF THE q-GENOCCHI POLYNOMIALS

  • Ryoo, Cheon-Seoung
    • Journal of applied mathematics & informatics
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    • 제28권5_6호
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    • pp.1277-1284
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    • 2010
  • One purpose of this paper is to consider the reflection symmetries of the q-Genocchi polynomials $G^*_{n,q}(x)$. We also observe the structure of the roots of q-Genocchi polynomials, $G^*_{n,q}(x)$, using numerical investigation. By numerical experiments, we demonstrate a remarkably regular structure of the real roots of $G^*_{n,q}(x)$.

SOME IDENTITIES OF THE GENOCCHI NUMBERS AND POLYNOMIALS ASSOCIATED WITH BERNSTEIN POLYNOMIALS

  • Lee, H.Y.;Jung, N.S.;Ryoo, C.S.
    • Journal of applied mathematics & informatics
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    • 제29권5_6호
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    • pp.1221-1228
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    • 2011
  • Recently, several mathematicians have studied some interesting relations between extended q-Euler number and Bernstein polynomials(see [3, 5, 7, 8, 10]). In this paper, we give some interesting identities on the Genocchi polynomials and Bernstein polynomials.

q-EXTENSIONS OF GENOCCHI NUMBERS

  • CENKCI MEHMET;CAN MUMUN;KURT VELI
    • 대한수학회지
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    • 제43권1호
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    • pp.183-198
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    • 2006
  • In this paper q-extensions of Genocchi numbers are defined and several properties of these numbers are presented. Properties of q-Genocchi numbers and polynomials are used to construct q-extensions of p-adic measures which yield to obtain p-adic interpolation functions for q-Genocchi numbers. As an application, general systems of congruences, including Kummer-type congruences for q-Genocchi numbers are proved.

A NOTE ON GENOCCHI-ZETA FUNCTIONS

  • Park, Kyoung-Ho
    • 호남수학학술지
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    • 제31권3호
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    • pp.399-405
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    • 2009
  • In this paper, we study the Genoochi-zeta functions which are entire functions in whole complex s-plane these zeta functions have the values of the Genocchi numbers and the Genoochi polynomials at negative integers respectively. That is ${\zeta}_G(1-k)={\frac{G_k}{k}}$ and ${\zeta}_G(1-k,x)={\frac{G_k(x)}{k}}$.

A NOTE ON MIXED POLYNOMIALS AND NUMBERS

  • Mohd Ghayasuddin;Nabiullah Khan
    • 호남수학학술지
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    • 제46권2호
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    • pp.168-180
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    • 2024
  • The main object of this article is to propose a unified extension of Bernoulli, Euler and Genocchi polynomials by means of a new family of mixed polynomials whose generating function is given in terms of generalized Bessel function. We also discuss here some fundamental properties of our introduced mixed polynomials by making use of the series arrangement technique. Furthermore, some conclusions of our present study are also pointed out in the last section.

NOTES ON THE PARAMETRIC POLY-TANGENT POLYNOMIALS

  • KURT, BURAK
    • Journal of applied mathematics & informatics
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    • 제38권3_4호
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    • pp.301-309
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    • 2020
  • Recently, M. Masjed-Jamai et al. in ([6]-[7]) and Srivastava et al. in ([15]-[16]) considered the parametric type of the Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials. They proved some theorems and gave some identities and relations for these polynomials. In this work, we define the parametric poly-tangent numbers and polynomials. We give some relations and identities for the parametric poly-tangent polynomials.

q-ADDITION THEOREMS FOR THE q-APPELL POLYNOMIALS AND THE ASSOCIATED CLASSES OF q-POLYNOMIALS EXPANSIONS

  • Sadjang, Patrick Njionou
    • 대한수학회지
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    • 제55권5호
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    • pp.1179-1192
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    • 2018
  • Several addition formulas for a general class of q-Appell sequences are proved. The q-addition formulas, which are derived, involved not only the generalized q-Bernoulli, the generalized q-Euler and the generalized q-Genocchi polynomials, but also the q-Stirling numbers of the second kind and several general families of hypergeometric polynomials. Some q-umbral calculus generalizations of the addition formulas are also investigated.