Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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A NOTE ON THE WEIGHTED q-GENOCCHI NUMBERS AND POLYNOMIALS WITH THEIR INTERPOLATION FUNCTION

  • Arac, Serkan (Department of Mathematics, Faculty of Science and Arts, University of Gaziantep) ;
  • Ackgoz, Mehmet (Department of Mathematics, Faculty of Science and Arts, University of Gaziantep) ;
  • Seo, Jong-Jin (Department of Applied Mathematics, Pukyong National University)
  • Received : 2011.09.28
  • Accepted : 2011.10.31
  • Published : 2012.03.25
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Abstract

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.

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References

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Cited by

  1. A NOTE ON THE q-ANALOGUE OF KIM'S p-ADIC log GAMMA TYPE FUNCTIONS ASSOCIATED WITH q-EXTENSION OF GENOCCHI AND EULER NUMBERS WITH WEIGHT α vol.50, pp.2, 2013, https://doi.org/10.4134/BKMS.2013.50.2.583
  2. ANALYTIC CONTINUATION OF WEIGHTED q-GENOCCHI NUMBERS AND POLYNOMIALS vol.28, pp.3, 2013, https://doi.org/10.4134/CKMS.2013.28.3.457