Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2006, Volume 324, Issue 2, pp. 790 - 804

In this paper, by using q-Volkenborn integral, we construct new generating functions of the new twisted ( h , q ) -Bernoulli polynomials and numbers. By...

Twisted q-zeta function | q-Volkenborn integral | q-Bernoulli numbers and polynomials | Twisted q-Bernoulli numbers and polynomials | q-zeta function | Twisted q- L-functions | L-function | Twisted q-L-functions | Q-ANALOG | MATHEMATICS | twisted q-L-functions | MATHEMATICS, APPLIED | SERIES | twisted q-zeta function | twisted q-Bernoulli numbers and polynomials | Q-ZETA FUNCTIONS

Twisted q-zeta function | q-Volkenborn integral | q-Bernoulli numbers and polynomials | Twisted q-Bernoulli numbers and polynomials | q-zeta function | Twisted q- L-functions | L-function | Twisted q-L-functions | Q-ANALOG | MATHEMATICS | twisted q-L-functions | MATHEMATICS, APPLIED | SERIES | twisted q-zeta function | twisted q-Bernoulli numbers and polynomials | Q-ZETA FUNCTIONS

Journal Article

Advances in Difference Equations, ISSN 1687-1839, 12/2015, Volume 2015, Issue 1, pp. 1 - 9

The p-adic q-integral (sometimes called q-Volkenborn integration) was defined by Kim. From p-adic q-integral equations, we can derive various q-extensions of...

(h, q)-Daehee numbers | p-adic q-integral | (h, q)-Bernoulli polynomials | (h, q)-Daehee polynomials | MATHEMATICS | MATHEMATICS, APPLIED | Q-BERNOULLI NUMBERS | DAEHEE | Integral equations | Analysis | Polynomials | Texts | Difference equations | Mathematical analysis

(h, q)-Daehee numbers | p-adic q-integral | (h, q)-Bernoulli polynomials | (h, q)-Daehee polynomials | MATHEMATICS | MATHEMATICS, APPLIED | Q-BERNOULLI NUMBERS | DAEHEE | Integral equations | Analysis | Polynomials | Texts | Difference equations | Mathematical analysis

Journal Article

Applicable Analysis and Discrete Mathematics, ISSN 1452-8630, 4/2018, Volume 12, Issue 1, pp. 1 - 35

The main purpose of this paper is to construct new families of special numbers with their generating functions. These numbers are related to many well-known...

Integers | Numbers | Generating function | Factorials | Discrete mathematics | Polynomials | Coefficients | Combinatorics | New family | Combinatorial sum | Central factorial numbers | Bernoulli numbers | Binomial coefficients | Euler numbers | Functional equations | Generating functions | Array polynomials | Stirling numbers | Fibonacci numbers | MATHEMATICS, APPLIED | COMBINATORIAL SUMS | Q-BERNOULLI NUMBERS | GENERATING-FUNCTIONS | MATHEMATICS

Integers | Numbers | Generating function | Factorials | Discrete mathematics | Polynomials | Coefficients | Combinatorics | New family | Combinatorial sum | Central factorial numbers | Bernoulli numbers | Binomial coefficients | Euler numbers | Functional equations | Generating functions | Array polynomials | Stirling numbers | Fibonacci numbers | MATHEMATICS, APPLIED | COMBINATORIAL SUMS | Q-BERNOULLI NUMBERS | GENERATING-FUNCTIONS | MATHEMATICS

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2019, Volume 2019, Issue 1, pp. 1 - 15

The Changhee numbers and polynomials are introduced by Kim, Kim and Seo (Adv. Stud. Theor. Phys. 7(20):993–1003, 2013), and the generalizations of those...

Fermionic p -adic q -integral on Z p ${\mathbb{Z}}_{p} | Analysis | Mathematics, general | ( h , q ) $(h,q)$ -Euler polynomials | Mathematics | Applications of Mathematics | Degenerate ( h , q ) $(h,q)$ -Changhee polynomials | Degenerate (h, q) -Changhee polynomials | (h, q) -Euler polynomials | Fermionic p-adic q-integral on Z | Q-EULER POLYNOMIALS | INTEGRALS | MATHEMATICS | MATHEMATICS, APPLIED | HIGHER-ORDER | IDENTITIES | (h, q)-Euler polynomials | Q-BERNOULLI | Degenerate (h, q)-Changhee polynomials | Fermionic p-adic q-integral on Z(p) | Polynomials | Fermionic p-adic q-integral on Z p ${\mathbb{Z}}_{p}

Fermionic p -adic q -integral on Z p ${\mathbb{Z}}_{p} | Analysis | Mathematics, general | ( h , q ) $(h,q)$ -Euler polynomials | Mathematics | Applications of Mathematics | Degenerate ( h , q ) $(h,q)$ -Changhee polynomials | Degenerate (h, q) -Changhee polynomials | (h, q) -Euler polynomials | Fermionic p-adic q-integral on Z | Q-EULER POLYNOMIALS | INTEGRALS | MATHEMATICS | MATHEMATICS, APPLIED | HIGHER-ORDER | IDENTITIES | (h, q)-Euler polynomials | Q-BERNOULLI | Degenerate (h, q)-Changhee polynomials | Fermionic p-adic q-integral on Z(p) | Polynomials | Fermionic p-adic q-integral on Z p ${\mathbb{Z}}_{p}

Journal Article

Advances in Difference Equations, ISSN 1687-1839, 08/2013, Volume 2013

In this paper, a further investigation for the Carlitz's q-Bernoulli numbers and q-Bernoulli polynomials is performed, and several symmetric identities for...

Q-Bernoulli numbers and polynomials | Bernoulli numbers and polynomials | Combinatorial identities | MATHEMATICS | MATHEMATICS, APPLIED | APOSTOL-TYPE | EULER POLYNOMIALS | q-Bernoulli numbers and polynomials | RECURRENCE | combinatorial identities | Usage | Polynomials | Dynamical systems | Analysis | Differential equations

Q-Bernoulli numbers and polynomials | Bernoulli numbers and polynomials | Combinatorial identities | MATHEMATICS | MATHEMATICS, APPLIED | APOSTOL-TYPE | EULER POLYNOMIALS | q-Bernoulli numbers and polynomials | RECURRENCE | combinatorial identities | Usage | Polynomials | Dynamical systems | Analysis | Differential equations

Journal Article

Taiwanese Journal of Mathematics, ISSN 1027-5487, 2/2011, Volume 15, Issue 1, pp. 241 - 257

The main object of this paper is to give -extensions of several explicit relationships of H. M. Srivastava and Á. Pintér [ (2004), 375-380] between the...

Polynomials | Mathematics | Q-bernoulli polynomials | Euler polynomials | Bernoulli polynomials | Recurrence relationships | NUMBERS | q-Extensions | q-Euler polynomials | Kronecker symbol | MATHEMATICS | ZETA | Difference equations | q-Bernoulli numbers | q-Stirling numbers of the second kind | APOSTOL-BERNOULLI | q-Bernoulli polynomials | q-Euler numbers | Addition theorems | FORMULAS

Polynomials | Mathematics | Q-bernoulli polynomials | Euler polynomials | Bernoulli polynomials | Recurrence relationships | NUMBERS | q-Extensions | q-Euler polynomials | Kronecker symbol | MATHEMATICS | ZETA | Difference equations | q-Bernoulli numbers | q-Stirling numbers of the second kind | APOSTOL-BERNOULLI | q-Bernoulli polynomials | q-Euler numbers | Addition theorems | FORMULAS

Journal Article

Abstract and Applied Analysis, ISSN 1085-3375, 04/2008, Volume 2008, pp. 1 - 11

For s∈ℂ, the Euler zeta function and the Hurwitz-type Euler zeta function are defined by ζE(s)=2∑n=1∞((−1)n/ns), and ζE(s,x)=2∑n=0∞((−1)n/(n+x)s). Thus, we...

MATHEMATICS | Q-BERNOULLI NUMBERS | MATHEMATICS, APPLIED | SERIES | SUMS | Prime numbers | Integral equations | Mathematics - Number Theory

MATHEMATICS | Q-BERNOULLI NUMBERS | MATHEMATICS, APPLIED | SERIES | SUMS | Prime numbers | Integral equations | Mathematics - Number Theory

Journal Article

Journal of Applied Mathematics, ISSN 1110-757X, 10/2013, Volume 2013, pp. 1 - 10

Recently, many mathematicians have studied different kinds of the Euler, Bernoulli, and Genocchi numbers and polynomials. In this paper, we give another...

MATHEMATICS, APPLIED | TWISTED (H | EXTENSION | INTERPOLATION FUNCTIONS | Q)-BERNOULLI NUMBERS | Sequences (Mathematics) | Polynomials | Research | Mathematical research | Number theory | Planes | Factorials | Mathematical analysis | Scattering | Combinatorial analysis

MATHEMATICS, APPLIED | TWISTED (H | EXTENSION | INTERPOLATION FUNCTIONS | Q)-BERNOULLI NUMBERS | Sequences (Mathematics) | Polynomials | Research | Mathematical research | Number theory | Planes | Factorials | Mathematical analysis | Scattering | Combinatorial analysis

Journal Article

Journal of Difference Equations and Applications, ISSN 1023-6198, 12/2008, Volume 14, Issue 12, pp. 1267 - 1277

The main purpose of this paper is to investigate several further interesting properties of symmetry for the p-adic invariant integrals on Zp. From these...

q-Volkenborn integrals | q-Euler numbers | q-stirling numbers | q-Bernoulli numbers

q-Volkenborn integrals | q-Euler numbers | q-stirling numbers | q-Bernoulli numbers

Journal Article

Symmetry, ISSN 2073-8994, 2018, Volume 10, Issue 10, p. 451

The q-Bernoulli numbers and polynomials can be given by Witt's type formulas as p-adic invariant integrals on Z(p). We investigate some properties for them. In...

P-adic integral on ℤ | Q-Bernoulli numbers | Two variable q-Bernstein polynomials | Q-Bernoulli polynomials | Two variable q-Bernstein operators | q-Bernoulli polynomials | two variable q-Bernstein polynomials | q-Bernoulli numbers | two variable q-Bernstein operators | MULTIDISCIPLINARY SCIENCES | p-adic integral on Z(p) | p-adic integral on ℤp

P-adic integral on ℤ | Q-Bernoulli numbers | Two variable q-Bernstein polynomials | Q-Bernoulli polynomials | Two variable q-Bernstein operators | q-Bernoulli polynomials | two variable q-Bernstein polynomials | q-Bernoulli numbers | two variable q-Bernstein operators | MULTIDISCIPLINARY SCIENCES | p-adic integral on Z(p) | p-adic integral on ℤp

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 2008, Volume 56, Issue 4, pp. 898 - 908

In [H. Ozden, Y. Simsek, I.N. Cangul, Generating functions of the ( h , q ) -extension of Euler polynomials and numbers, Acta Math. Hungarica, in press...

Twisted [formula omitted]-Euler numbers and polynomials | [formula omitted]-adic [formula omitted]-deformed fermionic integral | Zeta and [formula omitted]-functions | Twisted [formula omitted]-adic [formula omitted]- [formula omitted]-functions | p-adic q-deformed fermionic integral | Twisted p-adic (h, q)-l-functions | Zeta and l-functions | Twisted q-Euler numbers and polynomials | Q-ANALOG | MATHEMATICS, APPLIED | ADIC Q-INTEGRALS | BEHAVIOR | Z(P) | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Q)-BERNOULLI NUMBERS | Q-BERNOULLI POLYNOMIALS | L-SERIES | Integers | Interpolation | Presses | Construction | Integrals | Mathematical analysis | Mathematical models

Twisted [formula omitted]-Euler numbers and polynomials | [formula omitted]-adic [formula omitted]-deformed fermionic integral | Zeta and [formula omitted]-functions | Twisted [formula omitted]-adic [formula omitted]- [formula omitted]-functions | p-adic q-deformed fermionic integral | Twisted p-adic (h, q)-l-functions | Zeta and l-functions | Twisted q-Euler numbers and polynomials | Q-ANALOG | MATHEMATICS, APPLIED | ADIC Q-INTEGRALS | BEHAVIOR | Z(P) | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Q)-BERNOULLI NUMBERS | Q-BERNOULLI POLYNOMIALS | L-SERIES | Integers | Interpolation | Presses | Construction | Integrals | Mathematical analysis | Mathematical models

Journal Article

Bulletin of the Korean Mathematical Society, ISSN 1015-8634, 2015, Volume 52, Issue 3, pp. 741 - 749

The Changhee polynomials and numbers are introduced in [6]. Some interesting identities and properties of those polynomials are derived from umbral calculus...

Euler numbers | Changhee numbers | Twisted changhee numbers | MATHEMATICS | Q-BERNOULLI POLYNOMIALS | ADIC Q-INTEGRALS | twisted Changhee numbers

Euler numbers | Changhee numbers | Twisted changhee numbers | MATHEMATICS | Q-BERNOULLI POLYNOMIALS | ADIC Q-INTEGRALS | twisted Changhee numbers

Journal Article

Abstract and Applied Analysis, ISSN 1085-3375, 02/2008, Volume 2008

The aim of this paper, firstly, is to construct generating functions of q-Euler numbers and polynomials of higher order by applying the fermionic p-adic...

MATHEMATICS, APPLIED | TWISTED (H | BERNOULLI | PRODUCTS | Q)-BERNOULLI NUMBERS | SUMS

MATHEMATICS, APPLIED | TWISTED (H | BERNOULLI | PRODUCTS | Q)-BERNOULLI NUMBERS | SUMS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 01/2013, Volume 397, Issue 2, pp. 522 - 528

In this paper, by expressing the sums of products of the extended q-Euler polynomials in terms of the special values of the alternating multiple Hurwitz q-zeta...

[formula omitted]-Stirling numbers of the first kind | Alternating multiple Hurwitz [formula omitted]-zeta functions | Alternating Hurwitz [formula omitted]-zeta functions | Extended [formula omitted]-Euler numbers and polynomials | Sums of products | Higher-order extended [formula omitted]-Euler numbers and polynomials | Alternating Hurwitz q-zeta functions | Q-Stirling numbers of the first kind | Extended q-Euler numbers and polynomials | Higher-order extended q-Euler numbers and polynomials | Alternating multiple Hurwitz q-zeta functions | MATHEMATICS | MATHEMATICS, APPLIED | Q-BERNOULLI NUMBERS | q-Stirling numbers of the first kind

[formula omitted]-Stirling numbers of the first kind | Alternating multiple Hurwitz [formula omitted]-zeta functions | Alternating Hurwitz [formula omitted]-zeta functions | Extended [formula omitted]-Euler numbers and polynomials | Sums of products | Higher-order extended [formula omitted]-Euler numbers and polynomials | Alternating Hurwitz q-zeta functions | Q-Stirling numbers of the first kind | Extended q-Euler numbers and polynomials | Higher-order extended q-Euler numbers and polynomials | Alternating multiple Hurwitz q-zeta functions | MATHEMATICS | MATHEMATICS, APPLIED | Q-BERNOULLI NUMBERS | q-Stirling numbers of the first kind

Journal Article

Symmetry, ISSN 2073-8994, 08/2018, Volume 10, Issue 8, p. 311

We study a q-analogue of Euler numbers and polynomials naturally arising from the p-adic fermionic integrals on Z(p) and investigate some properties for these...

Q-Euler number | Q-Euler polynomial | Two variable q-Berstein operator | Two variable q-Berstein polynomial | APPROXIMATION | two variable q-Berstein operator | MULTIDISCIPLINARY SCIENCES | q-Euler polynomial | Q-BERNOULLI NUMBERS | q-Euler number | GREATER-THAN 1 | OPERATORS | two variable q-Berstein polynomial

Q-Euler number | Q-Euler polynomial | Two variable q-Berstein operator | Two variable q-Berstein polynomial | APPROXIMATION | two variable q-Berstein operator | MULTIDISCIPLINARY SCIENCES | q-Euler polynomial | Q-BERNOULLI NUMBERS | q-Euler number | GREATER-THAN 1 | OPERATORS | two variable q-Berstein polynomial

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2007, Volume 2008, Issue 1, pp. 1 - 8

The main purpose of this paper is to construct generating functions of higher-order twisted -extension of Euler polynomials and numbers, by using -adic,...

Mathematics, general | Mathematics | Applications of Mathematics | Analysis | MATHEMATICS | MATHEMATICS, APPLIED | TWISTED (H | Q)-BERNOULLI NUMBERS | Q-BERNOULLI NUMBERS | L-SERIES | Z(P) | Colleges & universities

Mathematics, general | Mathematics | Applications of Mathematics | Analysis | MATHEMATICS | MATHEMATICS, APPLIED | TWISTED (H | Q)-BERNOULLI NUMBERS | Q-BERNOULLI NUMBERS | L-SERIES | Z(P) | Colleges & universities

Journal Article

Advances in Difference Equations, ISSN 1687-1839, 12/2012, Volume 2012, Issue 1, pp. 1 - 10

In this article, we first aim to give simple proofs of known formulae for the generalized Carlitz q-Bernoulli polynomials β m,χ (x, q) in the p-adic case by...

Carlitz q -Bernoulli polynomials | Ordinary Differential Equations | Functional Analysis | Dirichlet q-L- functions | Analysis | Difference and Functional Equations | Mathematics, general | Mathematics | Carlitz q -Bernoulli numbers | Partial Differential Equations | Carlitz q-Bernoulli polynomials | Carlitz q-Bernoulli numbers | Dirichlet q-Lfunctions | Q-ANALOG | MATHEMATICS | MATHEMATICS, APPLIED | ZETA-FUNCTION | Dirichlet q-L-functions | Functions (mathematics) | Integers | Difference equations | Mathematical analysis | Classification | Proving | Polynomials

Carlitz q -Bernoulli polynomials | Ordinary Differential Equations | Functional Analysis | Dirichlet q-L- functions | Analysis | Difference and Functional Equations | Mathematics, general | Mathematics | Carlitz q -Bernoulli numbers | Partial Differential Equations | Carlitz q-Bernoulli polynomials | Carlitz q-Bernoulli numbers | Dirichlet q-Lfunctions | Q-ANALOG | MATHEMATICS | MATHEMATICS, APPLIED | ZETA-FUNCTION | Dirichlet q-L-functions | Functions (mathematics) | Integers | Difference equations | Mathematical analysis | Classification | Proving | Polynomials

Journal Article

Abstract and Applied Analysis, ISSN 1085-3375, 07/2008, Volume 2008, pp. 1 - 7

The main purpose of this paper is to study the distribution of Genocchi polynomials. Finally, we construct the Genocchi zeta function which interpolates...

MATHEMATICS, APPLIED | ZETA-FUNCTIONS | SERIES | Q-BERNOULLI NUMBERS | Q-EXTENSION | BACTERIAL | EULER | Numbers | Integral equations

MATHEMATICS, APPLIED | ZETA-FUNCTIONS | SERIES | Q-BERNOULLI NUMBERS | Q-EXTENSION | BACTERIAL | EULER | Numbers | Integral equations

Journal Article

Russian Journal of Mathematical Physics, ISSN 1061-9208, 7/2006, Volume 13, Issue 3, pp. 293 - 298

Recently, B. A. Kupershmidt constructed reflection symmetries of q-Bernoulli polynomials (see [12]). In this paper, we study new q-extensions of Euler numbers...

Mathematical and Computational Physics | Physics | Q-BERNOULLI POLYNOMIALS | GAMMA-FUNCTION | PHYSICS, MATHEMATICAL | MULTIPLE ZETA-FUNCTIONS

Mathematical and Computational Physics | Physics | Q-BERNOULLI POLYNOMIALS | GAMMA-FUNCTION | PHYSICS, MATHEMATICAL | MULTIPLE ZETA-FUNCTIONS

Journal Article

Abstract and Applied Analysis, ISSN 1085-3375, 12/2008, Volume 2008

Recently, Choi et al. (2008) have studied the q-extensions of the Apostol-Bernoulli and the Apostol-Euler polynomials of order n and multiple Hurwitz zeta...

MATHEMATICS | ORDER | MATHEMATICS, APPLIED | SERIES | GENOCCHI | LERCH ZETA-FUNCTIONS | Q-BERNOULLI NUMBERS | BACTERIAL | Computer science | Numbers | Mathematics

MATHEMATICS | ORDER | MATHEMATICS, APPLIED | SERIES | GENOCCHI | LERCH ZETA-FUNCTIONS | Q-BERNOULLI NUMBERS | BACTERIAL | Computer science | Numbers | Mathematics

Journal Article

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