A new generalization of the Genocchi numbers and its consequence on the Bernoulli polynomials

Identities on The Bernoulli and Genocchi Numbers and Polynomials

Let p be a fixed odd prime number. Throughout this paper Zp,Qp, and Cp will denote the ring of p-adic rational integers, the field of p-adic rational numbers, and the completion of the algebraic closure of Qp. Let N be the set of natural numbers and Z N ∪ {0}. The p-adic norm on Cp is normalized so that |p|p p−1. Let C Zp be the space of continuous functions on Zp. For f ∈ C Zp , the fermionic ...

On Genocchi Numbers and Polynomials

Let p be a fixed odd prime number. Throughout this paper, Zp, Qp, C, and Cp will, respectively, denote the ring of p-adic rational integers, the field of p-adic rationalnumbers, the complex number field, and the completion of the algebraic closure of Qp. Let vp be the normalized exponential valuation of Cp with |p|p p−vp p 1/p. When one talks about q-extension, q is variously considered as an i...

On the Multiple Sums of Bernoulli, Euler and Genocchi Polynomials

We introduce and investigate the Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials by means of a suitable theirs generating polynomials. We establish several interesting properties of these polynomials. Also, we gave some propositions two theorems and one corollary.

on the comparison of keyword and semantic-context methods of learning new vocabulary meaning

the rationale behind the present study is that particular learning strategies produce more effective results when applied together. the present study tried to investigate the efficiency of the semantic-context strategy alone with a technique called, keyword method. to clarify the point, the current study seeked to find answer to the following question: are the keyword and semantic-context metho...

Integral Formulae of Bernoulli and Genocchi Polynomials