• 제목/요약/키워드: Genocchi numbers and polynomials

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CALCULATING ZEROS OF THE GENERALIZED GENOCCHI POLYNOMIALS

  • Agarwal, R.P.;Ryoo, C.S.
    • Journal of applied mathematics & informatics
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    • 제27권3_4호
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    • pp.453-462
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    • 2009
  • Kim [4] defined the generalized Genocchi numbers $G_{n,x}$. In this paper, we introduce the generalized Genocchi polynomials $G_{n,x}(x)$. One purpose of this paper is to investigate the zeros of the generalized Genocchi polynomials $G_{n,x}(x)$. We also display the shape of generalized Genocchi polynomials $G_{n,x}(x)$.

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A NUMERICAL INVESTIGATION ON THE ZEROS OF THE GENOCCHI POLYNOMIALS

  • Ryoo C.S.
    • Journal of applied mathematics & informatics
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    • 제22권1_2호
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    • pp.125-132
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    • 2006
  • It is the aim of this paper to introduce the Genocchi numbers Gn and polynomials Gn(x) and to display the shape of Genocchi polynomials Gn(x). Finally, we investigate the roots of the Genocchi polynomials Gn(x).

AN EXTENSION OF GENERALIZED EULER POLYNOMIALS OF THE SECOND KIND

  • Kim, Y.H.;Jung, H.Y.;Ryoo, C.S.
    • Journal of applied mathematics & informatics
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    • 제32권3_4호
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    • pp.465-474
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    • 2014
  • Many mathematicians have studied various relations beween Euler number $E_n$, Bernoulli number $B_n$ and Genocchi number $G_n$ (see [1-18]). They have found numerous important applications in number theory. Howard, T.Agoh, S.-H.Rim have studied Genocchi numbers, Bernoulli numbers, Euler numbers and polynomials of these numbers [1,5,9,15]. T.Kim, M.Cenkci, C.S.Ryoo, L. Jang have studied the q-extension of Euler and Genocchi numbers and polynomials [6,8,10,11,14,17]. In this paper, our aim is introducing and investigating an extension term of generalized Euler polynomials. We also obtain some identities and relations involving the Euler numbers and the Euler polynomials, the Genocchi numbers and Genocchi polynomials.

CERTAIN RESULTS ON THE q-GENOCCHI NUMBERS AND POLYNOMIALS

  • Seo, Jong Jin
    • 충청수학회지
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    • 제26권1호
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    • pp.231-242
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    • 2013
  • In this work, we deal with $q$-Genocchi numbers and polynomials. We derive not only new but also interesting properties of the $q$-Genocchi numbers and polynomials. Also, we give Cauchy-type integral formula of the $q$-Genocchi polynomials and derive distribution formula for the $q$-Genocchi polynomials. In the final part, we introduce a definition of $q$-Zeta-type function which is interpolation function of the $q$-Genocchi polynomials at negative integers which we express in the present paper.

ANALYTIC CONTINUATION OF WEIGHTED q-GENOCCHI NUMBERS AND POLYNOMIALS

  • Araci, Serkan;Acikgoz, Mehmet;Gursul, Aynur
    • 대한수학회논문집
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    • 제28권3호
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    • pp.457-462
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    • 2013
  • In the present paper, we analyse analytic continuation of weighted $q$-Genocchi numbers and polynomials. A novel formula for weighted $q$-Genocchi-zeta function $\tilde{\zeta}_{G,q}(s{\mid}{\alpha})$ in terms of nested series of $\tilde{\zeta}_{G,q}(n{\mid}{\alpha})$ is derived. Moreover, we introduce a novel concept of dynamics of the zeros of analytically continued weighted $q$-Genocchi polynomials.

ON HIGHER ORDER (p, q)-FROBENIUS-GENOCCHI NUMBERS AND POLYNOMIALS

  • KHAN, WASEEM A.;KHAN, IDREES A.;KANG, J.Y.
    • Journal of applied mathematics & informatics
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    • 제37권3_4호
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    • pp.295-305
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    • 2019
  • In the present paper, we introduce (p, q)-Frobenius-Genocchi numbers and polynomials and investigate some basic identities and properties for these polynomials and numbers including addition theorems, difference equations, derivative properties, recurrence relations and so on. Then, we provide integral representations, implicit and explicit formulas and relations for these polynomials and numbers. We consider some relationships for (p, q)-Frobenius-Genocchi polynomials of order ${\alpha}$ associated with (p, q)-Bernoulli polynomials, (p, q)-Euler polynomials and (p, q)-Genocchi polynomials.