Fermionic P-adic Integral Research Articles

Novel identities involving Genocchi numbers and polynomials arising from applications of umbral calculus

The aim of this paper is to deal with applications of umbral calculus on fermionic p-adic integral on Zp. From those applications, we derive some new identities on Genocchi numbers and polynomials. Moreover, a systemic study of the class of Sheffer sequences on the generating function of Genocchi polynomials are given.

Higher-order Changhee numbers and polynomials

In this paper, we consider the higher-order Changhee numbers and polynomials which are derived from the fermionic p-adic integral on Zp and give some relations between higher-order Changhee polynomials and special polynomials.

A note on Changhee polynomials and numbers with q-parameter

In this paper, we consider the q-extensions of Changhee polynomials which are derived from the fermionic p-adic integral on Zp and the q-analogue of falling factorial sequence. Finally, we give some identities of those polynomials.

On p-adic Diamond–Euler Log Gamma functions

Abstract Text In this paper, using the fermionic p-adic integral on Z p , we define the corresponding p-adic Log Gamma functions, so-called p-adic Diamond–Euler Log Gamma functions. We then prove several fundamental results for these p-adic Log Gamma functions, including the Laurent series expansion, the distribution formula, the functional equation and the reflection formula. We express the derivative of p-adic Euler L-functions at s = 0 and the special values of p-adic Euler L-functions at positive integers as linear combinations of p-adic Diamond–Euler Log Gamma functions. Finally, using the p-adic Diamond–Euler Log Gamma functions, we obtain the formula for the derivative of the p-adic Hurwitz-type Euler zeta function at s = 0 , then we show that the p-adic Hurwitz-type Euler zeta functions will appear in the studying for a special case of p-adic analogue of the ( S , T ) -version of the abelian rank one Stark conjecture. Video For a video summary of this paper, please click here or visit http://youtu.be/DW77g3aPcFU .

On p -adic Hurwitz-type Euler zeta functions

The definition for the p-adic Hurwitz-type Euler zeta functions has been given by using the fermionic p-adic integral on Zp. By computing the values of this kind of p-adic zeta function at negative integers, we show that it interpolates the Euler polynomials p-adically. Many properties are provided for the p-adic Hurwitz-type Euler zeta functions, including the convergent Laurent series expansion, the distribution formula, the functional equation, the reflection formula, the derivative formula, the p-adic Raabe formula and so on. The definition for the p-adic Euler L-functions has also been given by using the p-adic Hurwitz-type Euler zeta functions.

On Carlitz's Type -Euler Numbers Associated with the Fermionic -Adic Integral on

We consider the following problem in the paper of Kim et al. (2010): Find Witt's formula for Carlitz's type -Euler numbers. We give Witt's formula for Carlitz's type -Euler numbers, which is an answer to the above problem. Moreover, we obtain a new p-adic q-l-function for Dirichlet's character , with the property that for using the fermionic p-adic integral on .

On Multiple Generalizedw-Genocchi Polynomials and Their Applications

We define the multiple generalizedw-Genocchi polynomials. By using fermionicp-adic invariant integrals, we derive some identities on these generalizedw-Genocchi polynomials, for example, fermionicp-adic integral representation, Witt's type formula, explicit formula, multiplication formula, and recurrence formula for thesew-Genocchi polynomials.

On q‐Euler Numbers Related to the Modified q‐Bernstein Polynomials

We consider q‐Euler numbers, polynomials, and q‐Stirling numbers of first and second kinds. Finally, we investigate some interesting properties of the modified q‐Bernstein polynomials related to q‐Euler numbers and q‐Stirling numbers by using fermionic p‐adic integrals on ℤp.

Some identities on the q-Euler polynomials of higher order and q-stirling numbers by the fermionic p-adic integral on ℤ p

A systemic study of some families of q-Euler numbers and families of polynomials of Norlund type is presented by using the multivariate fermionic p-adic integral on ℤ p . The study of these higher-order q-Euler numbers and polynomials yields an interesting q-analog of identities for Stirling numbers.

Symmetry p-adic invariant integral on ℤ p for Bernoulli and Euler polynomials

The main purpose of this paper is to investigate several further interesting properties of symmetry for the p-adic invariant integrals on ℤ p . From these symmetry, we can derive many interesting recurrence identities for Bernoulli and Euler polynomials. Finally we introduce the new concept of symmetry of fermionic p-adic invariant integral on ℤ p . By using this symmetry of fermionic p-adic invariant integral on ℤ p , we will give some relations of symmetry between the power sum polynomials and Euler numbers. The relation between the q-Bernoulli polynomials and q-Dedekind type sums which discussed in Y. Simsek (q-Dedekind type sums related to q-zeta function and basic L-series, J. Math. Anal. Appl. 318 (2006), pp. 333–351) can be also derived by using the properties of symmetry of fermionic p-adic integral on ℤ p .