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Introduction. Recently J. Rutkowski (see [3]) has defined the p-adic analogue of the Walsh system, which we shall denote by ${(ϕ ₘ)}_{m \in ℕ ₀}$ . The system ${(ϕ ₘ)}_{m \in ℕ ₀}$ is defined in the space C(ℤₚ,ℂₚ) of ℂₚ-valued continuous functions on ℤₚ. J. Rutkowski has also considered some questions concerning expansions of functions from C(ℤₚ,ℂₚ) with respect to ${(ϕ ₘ)}_{m \in ℕ ₀}$ . This paper is a remark to Rutkowski’s paper. We define another system ${(h ₙ)}_{n \in ℕ ₀}$ in C(ℤₚ,ℂₚ), investigate its properties and compare it to the system defined by Rutkowski. The system...

A note on the multiple twisted Carlitz's type $q$ -Bernoulli polynomials.

Jang, Lee-Chae, Ryoo, Cheon-Seoung (2008)

Abstract and Applied Analysis

A note on the $p$ -adic gamma function

Bernard Dwork (1981/1982)

Groupe de travail d'analyse ultramétrique

A note on the $q$ -Euler measures.

Kim, Taekyun, Hwang, Kyung-Won, Lee, Byungje (2009)

Advances in Difference Equations [electronic only]

A note on the $q$ -Genocchi numbers and polynomials.

Kim, Taekyun (2007)

Journal of Inequalities and Applications [electronic only]

A p-adic integral representation of the p-adic L-function.

Yasuo Morita (1978)

Journal für die reine und angewandte Mathematik

A p-adic measure attached to the zeta functions associated with two elliptic modular forms. I.

Haruzo Hida (1985)

Inventiones mathematicae

A representation theorem for a class of rigid analytic functions

Victor Alexandru, Nicolae Popescu, Alexandru Zaharescu (2003)

Journal de théorie des nombres de Bordeaux

Let $p$ be a prime number, $ℚ_{p}$ the field of $p$ -adic numbers and $ℂ_{p}$ the completion of the algebraic closure of $ℚ_{p}$ . In this paper we obtain a representation theorem for rigid analytic functions on $𝐏^{1} (ℂ_{p}) ∖ C (t, ϵ)$ which are equivariant with respect to the Galois group $G = G a l_{c o n t} (ℂ_{p} / ℚ_{p})$ , where $t$ is a lipschitzian element of $ℂ_{p}$ and $C (t, ϵ)$ denotes the $ϵ$ -neighborhood of the $G$ -orbit of $t$ .

A study on the $p$ -adic integral representation on $ℤ_{p}$ associated with Bernstein and Bernoulli polynomials.

Jang, Lee-Chae, Kim, Won-Joo, Simsek, Yilmaz (2010)

Advances in Difference Equations [electronic only]

A study on the $p$ -adic $q$ -integral representation on $ℤ_{p}$ associated with the weighted $q$ -Bernstein and $q$ -Bernoulli polynomials.

Kim, T., Bayad, A., Kim, Y.-H. (2011)

Journal of Inequalities and Applications [electronic only]

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A class number criterion for the equation $(x^{p} - 1) / (x - 1) = p y^{q}$

A new approach to $q$ -Bernoulli numbers and $q$ -Bernoulli polynomials related to $q$ -Bernstein polynomials.

A new $q$ -analogue of Bernoulli polynomials associated with $p$ -adic $q$ -integrals.

A note on Euler number and polynomials.

A note on functional equations of the $p$ -adic polylogarithms

A note on Nörlund-type twisted $q$ -Euler polynomials and numbers of higher order associated with fermionic invariant $q$ -integrals.

A note on some expansions of p-adic functions