• Title/Summary/Keyword: integral identities

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ON p-ADIC INTEGRAL FOR GENERALIZED DEGENERATE HERMITE-BERNOULLI POLYNOMIALS ATTACHED TO χ OF HIGHER ORDER

  • Khan, Waseem Ahmad;Haroon, Hiba
    • Honam Mathematical Journal
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    • v.41 no.1
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    • pp.117-133
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    • 2019
  • In the current investigation, we obtain the generating function for Hermite-based degenerate Bernoulli polynomials attached to ${\chi}$ of higher order using p-adic methods over the ring of integers. Useful identities, formulae and relations with well known families of polynomials and numbers including the Bernoulli numbers, Daehee numbers and the Stirling numbers are established. We also give identities of symmetry and additive property for Hermite-based generalized degenerate Bernoulli polynomials attached to ${\chi}$ of higher order. Results are supported by remarks and corollaries.

SOME IDENTITIES OF DEGENERATE GENOCCHI POLYNOMIALS

  • Lim, Dongkyu
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.2
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    • pp.569-579
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    • 2016
  • L. Carlitz introduced higher order degenerate Euler polynomials in [4, 5] and studied a degenerate Staudt-Clausen theorem in [4]. D. S. Kim and T. Kim gave some formulas and identities of degenerate Euler polynomials which are derived from the fermionic p-adic integrals on ${\mathbb{Z}}_p$ (see [9]). In this paper, we introduce higher order degenerate Genocchi polynomials. And we give some formulas and identities of degenerate Genocchi polynomials which are derived from the fermionic p-adic integrals on ${\mathbb{Z}}_p$.

SYMMETRIC IDENTITIES OF THE DEGENERATE MODIFIED q-EULER POLYNOMIALS UNDER THE SYMMETRIC GROUP

  • Kwon, Jongkyum;Pyo, Sung-Soo
    • Honam Mathematical Journal
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    • v.40 no.4
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    • pp.671-679
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    • 2018
  • Abstract of the article can be written hereAbstract of the article can be written here. Recently, several authors have studied the symmetric identities for special functions(see [3,5-11,14,17,18,20-22]). In this paper, we study the symmetric identities of the degenerate modified q-Euler polynomials under the symmetric group.

NOTE ON CAHEN′S INTEGRAL FORMULAS

  • Choi, June-Sang
    • Communications of the Korean Mathematical Society
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    • v.17 no.1
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    • pp.15-20
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    • 2002
  • We present an explicit form for a class of definite integrals whose special cases include some definite integrals evaluated, over a century ago, by Cahen who made use of an appropriate contour integral for the integrand of a well-known integral representation of the Riemann Zeta function given in (3). Furthermore another analogous class of definite integral formulas and some identities involving Riemann Zeta function and Euler numbers En are also obtained as by-products.

SOME PROPERTIES OF SPECIAL POLYNOMIALS WITH EXPONENTIAL DISTRIBUTION

  • Kang, Jung Yoog;Lee, Tai Sup
    • Communications of the Korean Mathematical Society
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    • v.34 no.2
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    • pp.383-390
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    • 2019
  • In this paper, we discuss special polynomials involving exponential distribution, which is related to life testing. We derive some identities of special polynomials such as the symmetric property, recurrence formula and so on. In addition, we investigate explicit properties of special polynomials by using their derivative and integral.

FURTHER HYPERGEOMETRIC IDENTITIES DEDUCIBLE BY FRACTIONAL CALCULUS

  • Gaboury, Sebastien;Rathie, Arjun K.
    • Communications of the Korean Mathematical Society
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    • v.29 no.3
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    • pp.429-437
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    • 2014
  • Motivated by the recent investigations of several authors, in this paper we present a generalization of a result obtained recently by Choi et al. ([3]) involving hypergeometric identities. The result is obtained by suitably applying fractional calculus method to a generalization of the hypergeometric transformation formula due to Kummer.

NOTES ON SOME IDENTITIES INVOLVING THE RIEMANN ZETA FUNCTION

  • Lee, Hye-Rim;Ok, Bo-Myoung;Choi, June-Sang
    • Communications of the Korean Mathematical Society
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    • v.17 no.1
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    • pp.165-173
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    • 2002
  • We first review Ramaswami's find Apostol's identities involving the Zeta function in a rather detailed manner. We then present corrected, or generalized formulas, or a different method of proof for some of them. We also give closed-form evaluation of some series involving the Riemann Zeta function by an integral representation of ζ(s) and Apostol's identities given here.