*Correspondence: [email protected] 2Graduate School of Education, Konkuk University, Seoul, 143-701, Republic of Korea Full list of author information is available at the end of the article Abstract In this paper, we study some properties of degenerate Changhee-Genocchi numbers and polynomials and give some new identities of these polynomials and numbers which are derived from the generating ...

Keywords: Genocchi numbers and polynomials q-Genocchi numbers von Staudt–Clausen's theorem Kummer congruence a b s t r a c t Recently, the von Staudt–Clausen's theorem for q-Euler numbers was introduced by Kim (2013) and q-Genocchi numbers were constructed by Araci et al. (2013). In this paper, we give the corresponding von Staudt–Clausen's theorem for q-Genocchi numbers and also get the Kummer...

The current article focus on the ordinary Bernoulli, Euler and Genocchi numbers and polynomials. It introduces a new approach to obtain identities involving these special polynomials and numbers via generating functions. As an application of the new approach, an easy proof for the main result in [6] is given. Relationships between the Genocchi and the Bernoulli polynomials and numbers are obtai...

We consider a natural generalization of the well studied Genocchi numbers This generalization proves useful in enumerating the class of deterministic nite automata DFA which accept a nite language We also link our generalization to the method of Gandhi polynomials for generating Genocchi numbers Introduction and Motivation The study of Genocchi numbers and their combinatorial interpretations ha...

This paper is well designed to set-up some new identities related generalized Apostol-type Hermite-based-Frobenius-Genocchi polynomials and by applying the generating functions, we derive implicit summation formulae symmetric identities. Further a relationship between Array-type polynomials, Bernoulli Frobenius-Genocchi also established.

Recently, the generalized Euler–Genocchi and degenerate polynomials are introduced. The aim of this note is to study multi-Euler–Genocchi which defined by means multiple logarithm generalize, respectively, polynomials. Especially, we express former polynomials, multi-Stirling numbers first kind Stirling second kind, latter kind.

By using the modified Milne-Thomson's polynomial given in Araci et al. (Appl Math Inf Sci 8(6):2803-2808, 2014), we introduce a new concept of the Apostol Hermite-Genocchi polynomials. We also perform a further investigation for aforementioned polynomial and derive some implicit summation formulae and general symmetric identities arising from different analytical means and generating functions ...

In this work, we define the generalized poly-Genocchi polynomials with the parameter a, b and c. We prove some properties for these polynomials. Also, we give closed formula and symmetry properties for these polynomials.

In this paper, we consider the degenerate Changhee-Genocchi polynomials and numbers, and give some identities for these numbers and polynomials. AMS subject classification: 11B68, 11S40, 11S80.

Recently, several Bell based polynomials such as Bernoulli, Euler, Genocchi and Apostol versions were defined investigated. The main aim of this paper is to introduce the general family Appell polynomials, which includes many new members in addition existing ones, investigate their properties including determinantal representation, recurrence relation, derivative formula, shift operators differ...