• 제목/요약/키워드: Genocchi polynomials

검색결과 38건 처리시간 0.024초

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.

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.

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.

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.

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.