We give some new formulae for product of two Genocchi polynomials including Euler polynomials and Bernoulli polynomials. Moreover, we derive some applications for Genocchi polynomials to study a matrix formulation.

/pdf/some-new-formulae-for-genocchi-numbers-and-polynomials-4dlrfp0yy4.pdf

Some New Formulae for Genocchi Numbers and Polynomials Involving Bernoulli and Euler Polynomials

In the present paper, we aim to specify a p-adic continuous function for an odd prime inside a p-adic q-analog of the extended Dedekind-type sums of higher order according to extended q-Euler polynomials (or weighted q-Euler polynomials) which is derived from a fermionic p-adic q-deformed integral on $\mathbb{Z}_{p}$
 .

/pdf/extended-q-dedekind-type-daehee-changhee-sums-associated-28xfio2qtr.pdf

Extended q-Dedekind-type Daehee-Changhee sums associated with extended q-Euler polynomials

In the present paper, our goal is to introduce a p-adic continuous function for an odd prime to inside a p-adic q-analogue of the higher order dedekind-type sums with weight alpha related to Extended q-Euler polynomials by using p-adic q-integral in the p-adic integer ring.

/pdf/extended-q-dedekind-type-daehee-changhee-sums-associated-2vn6n00a6m.pdf

Extended q-Dedekind-type Daehee-Changhee sums associated with Extended q-Euler polynomials

The objective of this paper is to derive the symmetric property of an (h, q)-zeta function with weight α. By using this property, we give some interesting identities for (h, q)-Genocchi polynomials with weight α. As a result, our applications possess a number of interesting properties which we state in this paper. MSC: 11S80; 11B68

/pdf/a-note-on-the-h-q-zeta-type-function-with-weight-a-3m527tgj0a.pdf

A note on the (h, q)-zeta-type function with weight α

In the present paper, the fundamental aim is to consider a p-adic continuous function for an odd prime to inside a p-adic q-analogue of the higher order modified Dedekind-type sums related to q-Genocchi polynomials with weight alpha by using fermionic p-adic invariant q-integral on Zp.

A note on the modified q-Dedekind sums

In this paper, we introduce the q-analogue of p-adic log gamma functions with weight alpha. Moreover, we give a relationship be- tween weighted p-adic q-log gamma functions and q-extension of Genocchi and Euler numbers with weight alpha. Assume that p is a fixed odd prime number. Throughout this paper Z, Zp, Qp and Cp will denote the ring of integers, the field of p-adic rational numbers and the completion of the algebraic closure of Qp, respectively. Also we denote N � = N ( {0} and exp(x) = e x . Let vp : Cp ! Q ( {1} (Q is the field of rational numbers) denote the p-adic valuation of Cp normalized so that vp (p) = 1. The absolute value on Cp will be denoted as |·|, and |x| p = p v p(x)

/pdf/a-note-on-the-q-analogue-of-kim-s-p-adic-log-gamma-type-1dau0266t7.pdf

A NOTE ON THE q-ANALOGUE OF KIM'S p-ADIC log GAMMA TYPE FUNCTIONS ASSOCIATED WITH q-EXTENSION OF GENOCCHI AND EULER NUMBERS WITH WEIGHT

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A NOTE ON THE q-ANALOGUE OF KIM'S p-ADIC log GAMMA TYPE FUNCTIONS ASSOCIATED WITH q-EXTENSION OF GENOCCHI AND EULER NUMBERS WITH WEIGHT