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ANALYTIC PROPERTIES OF THE q-VOLKENBORN INTEGRAL ON THE RING OF p-ADIC INTEGERS

  • Kim, Min-Soo (Department of Mathematics Kyungnam University) ;
  • Son, Jin-Woo (Department of Mathematics Kyungnam University)
  • Published : 2007.02.28

Abstract

In this paper, we consider the q-Volkenborn integral of uniformly differentiable functions on the p-adic integer ring. By using this integral, we obtain the generating functions of twisted q-generalized Bernoulli numbers and polynomials. We find some properties of these numbers and polynomials.

Keywords

q-Volkenborn integral;$I_q$-Fourier transforms

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  2. On Euler numbers, polynomials and related p-adic integrals vol.129, pp.9, 2009, https://doi.org/10.1016/j.jnt.2008.11.004
  3. Analysis of the p-adic q-Volkenborn integrals: An approach to generalized Apostol-type special numbers and polynomials and their applications vol.3, pp.1, 2016, https://doi.org/10.1080/23311835.2016.1269393
  4. Values of twisted Barnes zeta functions at negative integers vol.20, pp.2, 2013, https://doi.org/10.1134/S1061920813020015
  5. Some symmetric identities on higher order q-Euler polynomials and multivariate fermionic p-adic q-integral on Zp vol.221, 2013, https://doi.org/10.1016/j.amc.2013.06.088
  6. ( ρ , q )-Volkenborn integration vol.171, 2017, https://doi.org/10.1016/j.jnt.2016.07.019
  7. On (ρ,q)-Euler numbers and polynomials associated with (ρ,q)-Volkenborn integrals 2017, https://doi.org/10.1142/S179304211850015X
  8. A new approach to connect algebra with analysis: relationships and applications between presentations and generating functions vol.2013, pp.1, 2013, https://doi.org/10.1186/1687-2770-2013-51