##### Title: Identities on Genocchi Polynomials and Genocchi Numbers Concerning Binomial Coefficients

##### Pages: 140-146

##### Cite as:

Qing Zou, Identities on Genocchi Polynomials and Genocchi Numbers Concerning Binomial Coefficients, Int. J. Anal. Appl., 14 (2) (2017), 140-146.#### Abstract

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

##### Full Text: PDF

#### References

- 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.
- S. Araci, Novel identities for q-Genocchi numbers and polynomials, J. Funct. Spaces Appl. 2012 (2012), Article ID 214961.
- 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].
- S. Araci, Novel identities involving Genocchi numbers and polynomials arising from applications of umbral calculus, Appl. Math. Comput. 233 (2014), 599–607.
- 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.
- 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.
- 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.
- 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.
- 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.
- Y. He, Some new results on products of the Apostol–Genocchi polynomials, J. Comput. Anal. Appl. 22 (4) (2017), 591–600.
- D. Lim, Some identities of degenerate Genocchi polynomials, Bull. Korean Math. Soc. 53 (2) (2016), 569–579.
- 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.
- 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.
- L. Carlitz, q-Bernoulli numbers and polynomials, Duke Math. J. 15 (1948), 987–1000.
- 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.
- 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.
- 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.
- 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.
- T. Kim, Some identities for the Bernoulli, the Euler and the Genocchi numbers and polynomials, Adv. Stud. Contemp. Math. 20 (1) (2010), 23–28.
- Y. He and T. Kim, General convolution identities for Apostol-Bernoulli, Euler and Genocchi polynomials, J. Nonlinear Sci. Appl. 9 (2016), 4780–4797.
- T. Agoh, Convolution identities for Bernoulli and Genocchi polynomials, Electronic J. Combin. 21 (2014), Article ID P1.65.
- R. L. Graham. D. E. Knuth and O. Patashnik, Concrete mathematics — a foundation for computer science, 2nd edn. Addison-Wesley Publishing Company, Reading, 1994.