• Title/Summary/Keyword: Polylogarithm functions

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SOME IDENTITIES INVOLVING THE LEGENDRE'S CHI-FUNCTION

  • Choi, June-Sang
    • Communications of the Korean Mathematical Society
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    • v.22 no.2
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    • pp.219-225
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    • 2007
  • Since the time of Euler, the dilogarithm and polylogarithm functions have been studied by many mathematicians who used various notations for the dilogarithm function $Li_2(z)$. These functions are related to many other mathematical functions and have a variety of application. The main objective of this paper is to present corrected versions of two equivalent factorization formulas involving the Legendre's Chi-function $\chi_2$ and an evaluation of a class of integrals which is useful to evaluate some integrals associated with the dilogarithm function.

A NOTE ON THE GENERALIZED BERNOULLI POLYNOMIALS WITH (p, q)-POLYLOGARITHM FUNCTION

  • JUNG, N.S.
    • Journal of applied mathematics & informatics
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    • v.38 no.1_2
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    • pp.145-157
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    • 2020
  • In this article, we define a generating function of the generalized (p, q)-poly-Bernoulli polynomials with variable a by using the polylogarithm function. From the definition, we derive some properties that is concerned with other numbers and polynomials. Furthermore, we construct a special functions and give some symmetric identities involving the generalized (p, q)-poly-Bernoulli polynomials and power sums of the first integers.

A RESEARCH ON THE GENERALIZED POLY-BERNOULLI POLYNOMIALS WITH VARIABLE a

  • JUNG, Nam-Soon;RYOO, Cheon Seoung
    • Journal of applied mathematics & informatics
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    • v.36 no.5_6
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    • pp.475-489
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    • 2018
  • In this paper, by using the polylogarithm function, we introduce a generalized poly-Bernoulli numbers and polynomials with variable a. We find several combinatorial identities and properties of the polynomials. We give some properties that is connected with the Stirling numbers of second kind. Symmetric properties can be proved by new configured special functions. We display the zeros of the generalized poly-Bernoulli polynomials with variable a and investigate their structure.

A NOTE ON q-ANALOGUE OF POLY-BERNOULLI NUMBERS AND POLYNOMIALS

  • Hwang, Kyung Won;Nam, Bo Ryeong;Jung, Nam-Soon
    • Journal of applied mathematics & informatics
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    • v.35 no.5_6
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    • pp.611-621
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    • 2017
  • In this paper, we define a q-analogue of the poly-Bernoulli numbers and polynomials which is generalization of the poly Bernoulli numbers and polynomials including q-polylogarithm function. We also give the relations between generalized poly-Bernoulli polynomials. We derive some relations that are connected with the Stirling numbers of second kind. By using special functions, we investigate some symmetric identities involving q-poly-Bernoulli polynomials.

A STUDY OF POLY-BERNOULLI POLYNOMIALS ASSOCIATED WITH HERMITE POLYNOMIALS WITH q-PARAMETER

  • Khan, Waseem A.;Srivastava, Divesh
    • Honam Mathematical Journal
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    • v.41 no.4
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    • pp.781-798
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    • 2019
  • This paper is designed to introduce a Hermite-based-poly-Bernoulli numbers and polynomials with q-parameter. By making use of their generating functions, we derive several summation formulae, identities and some properties that is connected with the Stirling numbers of the second kind. Furthermore, we derive symmetric identities for Hermite-based-poly-Bernoulli polynomials with q-parameter by using generating functions.

SYMMETRIC IDENTITIES FOR DEGENERATE q-POLY-BERNOULLI NUMBERS AND POLYNOMIALS

  • JUNG, N.S.;RYOO, C.S.
    • Journal of applied mathematics & informatics
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    • v.36 no.1_2
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    • pp.29-38
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    • 2018
  • In this paper, we introduce a degenerate q-poly-Bernoulli numbers and polynomials include q-logarithm function. We derive some relations with this polynomials and the Stirling numbers of second kind and investigate some symmetric identities using special functions that are involving this polynomials.

NOTES ON THE PARAMETRIC POLY-TANGENT POLYNOMIALS

  • KURT, BURAK
    • Journal of applied mathematics & informatics
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    • v.38 no.3_4
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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.