A note on the modified q-Genocchi numbers and polynomials with weight (α, β)
2013
artykuł naukowy
angielski
- Genocchi numbers and polynomials
- q-Genocchi numbers and polynomials
- q-Genocchi numbers and polynomials with weight α
EN The purpose of this paper concerns to establish modified q-Genocchi numbers and polynomials with weight (α, β). In this paper we investigate special generalized q-Genocchi polynomials and we apply the method of generating function, which are exploited to derive further classes of q-Genocchi polynomials and develop q-Genocchi numbers and polynomials. By using the Laplace-Mellin transformation integral, we define q-Zeta function with weight (α, β) and by presenting a link between q-Zeta function with weight (α, β) and q-Genocchi numbers with weight (α, β) we obtain an interpolation formula for the q-Genocchi numbers and polynomials with weight (α, β). Also we derive distribution formula (Multiplication Theorem) and Witt’s type formula for modified q-Genocchi numbers and polynomials with weight (α, β) which yields a deeper insight into the effectiveness of this type of generalizations for q-Genocchi numbers and polynomials. Our new generating function possess a number of interesting properties which we state in this paper.
21 - 32
CC BY-NC-ND (uznanie autorstwa - użycie niekomercyjne - bez utworów zależnych)
publiczny
10