Identities on Genocchi Polynomials and Genocchi Numbers Concerning Binomial Coefficients

Main Article Content

Qing Zou


In this paper, the author gives some new identities on Genocchi polynomials and Genocchi numbers.

Article Details


  1. S. Araci, M. Acikgoz, H. Jolany and J. J. Seo, A unified generating function of the q-Genocchi polynomials with their interpolation functions, Proc. Jangjeon Math. Soc. 15 (2) (2012), 227-233.
  2. S. Araci, Novel identities for q-Genocchi numbers and polynomials, J. Funct. Spaces Appl. 2012 (2012), Article ID 214961.
  3. S. Araci, M. Acikgoz and E. Sen, Some new identities of Genocchi numbers and polynomials involving Bernoulli and Euler polynomials, arXiv:1209.0628 [math.NT].
  4. S. Araci, Novel identities involving Genocchi numbers and polynomials arising from applications of umbral calculus, Appl. Math. Comput. 233 (2014), 599-607.
  5. S. Araci, M. Acikgoz and E. Sen, On the von Staudt-Clausen's theorem associated with q-Genocchi numbers, Appl. Math. Comput. 247 (2014), 780-785.
  6. S. Araci, E. Sen and M. Acikgoz, Theorems on Genocchi polynomials of higher order arising from Genocchi basis, Taiwanese J. Math. 18 (2) (2014), 473-482.
  7. S. Araci, W. A. Khan, M. Acikgoz, C. Ozel and P. Kumam, A new generalization of Apostol type Hermite-Genocchi polynomials and its applications, Springerplus, 5 (2016), Art. ID 860.
  8. T. Kim, S. H. Rim, D. V. Dolgy and S. H. Lee, Some identities of Genocchi polynomials arising from Genocchi basis, J. Ineq. Appl. 2013 (2013), Article ID 43.
  9. Y. He, S. Araci, H. M. Srivastava and M. Acikgoz, Some new identities for the Apostol-Bernoulli polynomials and the Apostol-Genocchi polynomials, Appl. Math. Comput. 262 (2015), 31-41.
  10. Y. He, Some new results on products of the Apostol-Genocchi polynomials, J. Comput. Anal. Appl. 22 (4) (2017), 591-600.
  11. D. Lim, Some identities of degenerate Genocchi polynomials, Bull. Korean Math. Soc. 53 (2) (2016), 569-579.
  12. U. Duran, M. Acikgoz and S. Araci, Symmetric identities involving weighted q-Genocchi polynomials under S 4 , Proc. Jangjeon Math. Soc. 18 (4) (2015), 455-465.
  13. E. Agyuz, M. Acikgoz and S. Araci, A symmetric identity on the q-Genocchi polynomials of higher-order under third dihedral group D 3 , Proc. Jangjeon Math. Soc. 18 (2) (2015), 177-187.
  14. L. Carlitz, q-Bernoulli numbers and polynomials, Duke Math. J. 15 (1948), 987-1000.
  15. J. Choi and Y.-H. Kim, A note on high order Bernoulli numbers and polynomials using differential equations, Appl. Math. Comput. 249 (2014), 480-486.
  16. D. S. Kim, T. Kim and D. V. Dolgy, A note on degenerate Bernoulli numbers and polynomials associated with p-adic invariant integral on Z p , Appl. Math. Comput. 259 (2015), 198-204.
  17. J. Choi, P. J. Anderson and H. M. Srivastava, Carlitzs q-Bernoulli and q-Euler numbers and polynomials and a class of generalized q-Hurwitz zeta functions, Appl. Math. Comput. 215 (2009), 1185-1208.
  18. S. Araci, M. Acikgoz and E. Sen, Some new formulae for Genocchi numbers and polynomials involving Bernoulli and Euler polynomials, Int. J. Math. Math. Sci. 2014 (2014), Article ID 760613.
  19. T. Kim, Some identities for the Bernoulli, the Euler and the Genocchi numbers and polynomials, Adv. Stud. Contemp. Math. 20 (1) (2010), 23-28.
  20. Y. He and T. Kim, General convolution identities for Apostol-Bernoulli, Euler and Genocchi polynomials, J. Nonlinear Sci. Appl. 9 (2016), 4780-4797.
  21. T. Agoh, Convolution identities for Bernoulli and Genocchi polynomials, Electronic J. Combin. 21 (2014), Article ID P1.65.
  22. R. L. Graham. D. E. Knuth and O. Patashnik, Concrete mathematics ”” a foundation for computer science, 2nd edn. Addison-Wesley Publishing Company, Reading, 1994.