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A New Family of q-analogue of Genocchi Numbers and Polynomials of Higher Order

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In the present paper, we introduce thenew generalization of q-Genocchi polynomials and numbers ofhigher order. Also, we give some interesting identities. Finally, byapplying q-Mellin transformation to the generating function for q-Genocchi polynomials of higher order put we define novel q-Hurwitz-Zeta type function which is an interpolation forthis polynomials at negative integers.

Abstract

In the present paper, we introduce thenew generalization of q-Genocchi polynomials and numbers ofhigher order. Also, we give some interesting identities. Finally, byapplying q-Mellin transformation to the generating function for q-Genocchi polynomials of higher order put we define novel q-Hurwitz-Zeta type function which is an interpolation forthis polynomials at negative integers.

참고문헌 (27)

  1. S. Araci, "Novel identities involving Genocchi numbers and polynomials arising from applications of umbral calculus", Applied Mathematics and Computation, 233, pp.599~607 (2014)
  2. M. Acikgoz, "A note on the modied q-Bernstein polynomials for functions of several variables and their re ections on q-Volkenborn integration", Applied Mathematics and Computation, 218(3), pp.707~712 (2011)
  3. S. Araci, "On the extended Kim's p-adic q-deformed fermionic integrals in the p-adic integer ring", Journal of Number Theory, 133, pp.3348~3361 (2013)
  4. Serkan Araci, "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", 대한수학회보, 50(2), pp.583~588 (2013), 대한수학회
  5. S. Araci, "A study on the fermionic p-adic q-integral representation on Zp associated with weighted q-Bernstein and q-Genocchi polynomials", Abstract and Applied Analysis, 2011, pp.10~ (2011)
  6. Serkan Araci, "Analytic continuation of weighted q-Genocchi numbers and polynomials", 대한수학회논문집, 28(3), pp.457~462 (2013), 대한수학회
  7. S. Araci, "A note on the Frobenius-Euler numbers and polynomials associated with Bernstein polynomials", Advanced Studies in Contemporary Mathematics, 22(3), pp.399~406 (2012), 장전수학회
  8. Serkan Araci, "A unified generating function of the q-genocchi polynomials with their interpolation functions", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 15(2), pp.227~233 (2012), 장전수학회
  9. S. Araci, "New construction weighted (h; q)-Genocchi numbers and polynomials related to Zeta-type functions", Discrete Dynamics in Nature and Society, 2011, pp.7~ (2011)
  10. K. Brahim, "Some applications of the q-Mellin Transform", Tamsui Oxford Journal of Mathematical Sciences, 26(3), pp.335~343 (2010)
  11. Y. He, "Some formulae of products of the Apostol-Bernoulli and Apostol-Euler polynomials", Discrete Dynamics in Nature and Society, 2012, pp.11~ (2012)
  12. F. H. Jackson, "On q-denite integrals", The Quarterly Journal of Pure and Applied Mathematics, 41, pp.193~2036 (1910)
  13. 장이채, "THE q-ANALOGUE OF TWISTED LERCH TYPE EULER ZETA FUNCTIONS", 대한수학회보, 47(6), pp.1181~1188 (2010), 대한수학회
  14. H. Jolany, "Some results for Apostol-Genocchi Polynomials of higher order", Bulletin of the Malaysian Mathematical Sciences Society, 36(2) (2013)
  15. V. G. Kac, "Quantum Calculus, Universitext" (2002), Springer-Verlag
  16. T. Kim, "q-Generalized Euler numbers and polynomials", Russ. J. Math. Phys., 13(3), pp.293~308 (2006)
  17. T. Kim, "Some identities on the q-Euler polynomials of higher order and q-stirling numbers by the fermionic p-adic integral on Zp", Russian J. Math. Phys., 16, pp.484~491 (2009)
  18. T. Kim, "On the q-extension of Euler and Genocchi numbers", J. Math. Anal. Appl., 326, pp.1458~1465 (2007)
  19. T. Kim, "On the analogs of Euler numbers and polynomials associated with p-adic q-integral on Zp at q = −1", J. Math. Anal. Appl., 331, pp.779~792 (2007)
  20. T. Kim, "Some Identities on the integral representation of the product of several q-Bernstein-type polynomials", Abstract and Applied Analysis, 2011, pp.11~ (2011)
  21. T. Kim, "On the values of the weighted q-Zeta and L-functions", Discrete Dynamics in Nature and Society, 2011, pp.7~ (2011)
  22. T. Kim, "Euler numbers and polynomials associated with Zeta functions", Abstract and Applied Analysis, 2008, pp.11~ (2008)
  23. T. Kim, "Power series and asymptotic series associated with the q-analog of the twovariable p-adic L-function", Russian Journal of Mathematical Physics, 12(2), pp.186~196 (2005)
  24. T. Kim, "On the q-extension of Euler and Genocchi numbers", J. Math. Anal. Appl., 326, pp.1458~1465 (2007)
  25. "Notes on the Riemann's Zeta function"[URL]
  26. S-H. Rim, "On multiple interpolation functions of the q-Genocchi polynomials", Journal of Inequalities and Applications, 2010, pp.13~ (2010)
  27. Richard L. Rubin, "A q2-analogue operator for q²-analogue Fourier Analysis", J. Math. Analys. App., 212, pp.571~582 (1997)

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