• Title/Summary/Keyword: Euler polynomials

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SYMMETRIC IDENTITIES FOR DEGENERATE CARLITZ-TYPE q-EULER NUMBERS AND POLYNOMIALS

  • RYOO, CHEON SEOUNG
    • Journal of applied mathematics & informatics
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    • v.37 no.3_4
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    • pp.259-270
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    • 2019
  • In this paper we define the degenerate Carlitz-type q-Euler polynomials by generalizing the degenerate Euler numbers and polynomials, degenerate Carlitz-type Euler numbers and polynomials. We also give some interesting properties, explicit formulas, a connection with degenerate Carlitz-type q-Euler numbers and polynomials.

SOME PROPERTIES OF DEGENERATE CARLITZ-TYPE TWISTED q-EULER NUMBERS AND POLYNOMIALS

  • RYOO, CHEON SEOUNG
    • Journal of applied mathematics & informatics
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    • v.39 no.1_2
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    • pp.1-11
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    • 2021
  • In this paper, we define degenerate Carlitz-type twisted q-Euler numbers and polynomials by generalizing the degenerate Euler numbers and polynomials, Carlitz's type degenerate q-Euler numbers and polynomials. We also give some interesting properties, explicit formulas, symmetric properties, a connection with degenerate Carlitz-type twisted q-Euler numbers and polynomials.

ON THE (p, q)-ANALOGUE OF EULER ZETA FUNCTION

  • RYOO, CHEON SEOUNG
    • Journal of applied mathematics & informatics
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    • v.35 no.3_4
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    • pp.303-311
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    • 2017
  • In this paper we define (p, q)-analogue of Euler zeta function. In order to define (p, q)-analogue of Euler zeta function, we introduce the (p, q)-analogue of Euler numbers and polynomials by generalizing the Euler numbers and polynomials, Carlitz's type q-Euler numbers and polynomials. We also give some interesting properties, explicit formulas, a connection with (p, q)-analogue of Euler numbers and polynomials. Finally, we investigate the zeros of the (p, q)-analogue of Euler polynomials by using computer.

A NEW CLASS OF GENERALIZED APOSTOL-TYPE FROBENIUS-EULER-HERMITE POLYNOMIALS

  • Pathan, M.A.;Khan, Waseem A.
    • Honam Mathematical Journal
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    • v.42 no.3
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    • pp.477-499
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    • 2020
  • In this paper, we introduce a new class of generalized Apostol-type Frobenius-Euler-Hermite polynomials and derive some explicit and implicit summation formulae and symmetric identities by using different analytical means and applying generating functions. These results extend some known summations and identities of generalized Frobenius-Euler type polynomials and Hermite-based Apostol-Euler and Apostol-Genocchi polynomials studied by Pathan and Khan, Kurt and Simsek.

A NOTE ON THE q-EULER NUMBERS AND POLYNOMIALS WITH WEAK WEIGHT α AND q-BERNSTEIN POLYNOMIALS

  • Lee, H.Y.;Jung, N.S.;Kang, J.Y.
    • Journal of applied mathematics & informatics
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    • v.31 no.3_4
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    • pp.523-531
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    • 2013
  • In this paper we construct a new type of $q$-Bernstein polynomials related to $q$-Euler numbers and polynomials with weak weight ${\alpha}$ ; $E^{(\alpha)}_{n,q}$, $E^{(\alpha)}_{n,q}(x)$ respectively. Some interesting results and relationships are obtained.

A RESEARCH ON A NEW APPROACH TO EULER POLYNOMIALS AND BERNSTEIN POLYNOMIALS WITH VARIABLE [x]q

  • JUNG, NAM SOON;RYOO, CHEON SEOUNG
    • Journal of applied mathematics & informatics
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    • v.35 no.1_2
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    • pp.205-215
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    • 2017
  • In this paper, we consider a modified Euler polynomials ${\tilde{E}}_{n,q}(x)$ with variable $[x]_q$ and investigate some interesting properties of the Euler polynomials. We also give some relationships between the modified Euler polynomials and their Hurwitz zeta function. Finally, we derive some identities associated with Bernstein polynomials.

SYMMETRIC IDENTITIES INVOLVING THE MODIFIED (p, q)-HURWITZ EULER ZETA FUNCTION

  • KIM, A HYUN;AN, CHAE KYEONG;LEE, HUI YOUNG
    • Journal of applied mathematics & informatics
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    • v.36 no.5_6
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    • pp.555-565
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    • 2018
  • The main subject of this paper is to introduce the (p, q)-Euler polynomials and obtain several interesting symmetric properties of the modified (p, q)-Hurwitz Euler Zeta function with regard to (p, q) Euler polynomials. In order to get symmetric properties, we introduce the new (p, q)-analogue of Euler polynomials $E_{n,p,q}(x)$ and numbers $E_{n,p,q}$.

SOME PROPERTIES OF GENERALIZED q-POLY-EULER NUMBERS AND POLYNOMIALS WITH VARIABLE a

  • KIM, A HYUN
    • Journal of applied mathematics & informatics
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    • v.38 no.1_2
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    • pp.133-144
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    • 2020
  • In this paper, we discuss generalized q-poly-Euler numbers and polynomials. To do so, we define generalized q-poly-Euler polynomials with variable a and investigate its identities. We also represent generalized q-poly-Euler polynomials E(k)n,q(x; a) using Stirling numbers of the second kind. So we explore the relation between generalized q-poly-Euler polynomials and Stirling numbers of the second kind through it. At the end, we provide symmetric properties related to generalized q-poly-Euler polynomials using alternating power sum.