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A NOTE ON THE WEIGHTED q-GENOCCHI NUMBERS AND POLYNOMIALS WITH THEIR INTERPOLATION FUNCTION

Arac, Serkan;Ackgoz, Mehmet;Seo, Jong-Jin

  • Received : 2011.09.28
  • Accepted : 2011.10.31
  • Published : 2012.03.25

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.

Keywords

Genocchi numbers and polynomials;q-Genocchi numbers and polynomials;q-Genocchi numbers and polynomials with weight

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