01/2019, ISBN 9783039216215

.... Each paper presents mathematical theories, methods, and their application based on current and recently developed symmetric polynomials...

eBook

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 polynomials are characterized...

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 | (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 | (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

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, 7/2019, Volume 113, Issue 3, pp. 2913 - 2920

Here we consider the degenerate Bernstein polynomials as a degenerate version of Bernstein polynomials, which are motivated by Simsek’s recent work...

11B83 | Theoretical, Mathematical and Computational Physics | Degenerate Bernstein polynomials | Generating functions | Mathematics, general | Mathematics | Bernoulli polynomials | Applications of Mathematics | Stirling numbers | MATHEMATICS | Mathematical analysis | Polynomials | Combinatorial analysis

11B83 | Theoretical, Mathematical and Computational Physics | Degenerate Bernstein polynomials | Generating functions | Mathematics, general | Mathematics | Bernoulli polynomials | Applications of Mathematics | Stirling numbers | MATHEMATICS | Mathematical analysis | Polynomials | Combinatorial analysis

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 02/2016, Volume 274, pp. 258 - 266

We present several explicit formulas and recurrence relations for the degenerate Mittag-Leffler polynomials...

Falling factorial polynomials | Frobenius–Euler polynomials | Bernoulli polynomials | Umbral calculus | Degenerate Mittag-Leffler polynomials | Frobenius-Euler polynomials | MATHEMATICS, APPLIED | EULER POLYNOMIALS

Falling factorial polynomials | Frobenius–Euler polynomials | Bernoulli polynomials | Umbral calculus | Degenerate Mittag-Leffler polynomials | Frobenius-Euler polynomials | MATHEMATICS, APPLIED | EULER POLYNOMIALS

Journal Article

5.
Full Text
Identities for degenerate Bernoulli polynomials and Korobov polynomials of the first kind

Science China. Mathematics, ISSN 1869-1862, 2018, Volume 62, Issue 5, pp. 999 - 1028

In this paper, we derive five basic identities for Sheffer polynomials by using generalized Pascal functional and Wronskian matrices...

11B83 | 05A40 | degenerate Bernoulli polynomial | Krobov polynomial of the first kind | 05A19 | Mathematics | generalized Pascal functional matrix | Applications of Mathematics | Wronskian matrix | MATHEMATICS | MATHEMATICS, APPLIED

11B83 | 05A40 | degenerate Bernoulli polynomial | Krobov polynomial of the first kind | 05A19 | Mathematics | generalized Pascal functional matrix | Applications of Mathematics | Wronskian matrix | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Mathematica Slovaca, ISSN 0139-9918, 06/2018, Volume 68, Issue 3, pp. 527 - 536

We define a truncated Euler polynomial ) as a generalization of the classical Euler polynomial...

Secondary 11B83, 11B37, 05A15, 05A19 | truncated Euler polynomials | Bernoulli polynomials | Primary 11B68 | Euler polynomials | hypergeometric Bernoulli polynomials | Polynomials

Secondary 11B83, 11B37, 05A15, 05A19 | truncated Euler polynomials | Bernoulli polynomials | Primary 11B68 | Euler polynomials | hypergeometric Bernoulli polynomials | Polynomials

Journal Article

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, 4/2017, Volume 111, Issue 2, pp. 435 - 446

Recently, several authors have studied the degenerate Bernoulli and Euler polynomials and given some intersting identities of those polynomials...

11B83 | Degenerate Bell numbers and polynomials | Theoretical, Mathematical and Computational Physics | 11B73 | Mathematics, general | 05A19 | Mathematics | Degenerate Stirling numbers of the second kind | Applications of Mathematics | 11B37 | MATHEMATICS | BERNOULLI NUMBERS

11B83 | Degenerate Bell numbers and polynomials | Theoretical, Mathematical and Computational Physics | 11B73 | Mathematics, general | 05A19 | Mathematics | Degenerate Stirling numbers of the second kind | Applications of Mathematics | 11B37 | MATHEMATICS | BERNOULLI NUMBERS

Journal Article

中国科学：数学英文版, ISSN 1674-7283, 2015, Volume 58, Issue 10, pp. 1 - 10

We investigate Bell polynomials, also called Touchard polynomials or exponential polynomials, by using and without using umbral calculus...

恒等式 | 指数多项式 | 阶乘 | Bell多项式 | 贝尔 | 伯努利多项式 | 哑演算 | 柯西 | 11B83 | 05A40 | umbral calculus | Cauchy polynomial | 11B73 | higher-order Bernoulli polynomial | 05A19 | Mathematics | Applications of Mathematics | Bell-polynomial | poly-Bernoulli polynomial | MATHEMATICS | MATHEMATICS, APPLIED

恒等式 | 指数多项式 | 阶乘 | Bell多项式 | 贝尔 | 伯努利多项式 | 哑演算 | 柯西 | 11B83 | 05A40 | umbral calculus | Cauchy polynomial | 11B73 | higher-order Bernoulli polynomial | 05A19 | Mathematics | Applications of Mathematics | Bell-polynomial | poly-Bernoulli polynomial | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Abstract and applied analysis, ISSN 1085-3375, 03/2010, Volume 2010, pp. 1 - 12

The main object of this paper is to construct a new generating function of the (q-) Bernstein-type polynomials...

MATHEMATICS | MATHEMATICS, APPLIED | CONVERGENCE | TWISTED (H | APPROXIMATION | Q)-BERNOULLI NUMBERS | Studies | Binomial distribution | Polynomials | Numerical analysis | Derivatives | Computer graphics

MATHEMATICS | MATHEMATICS, APPLIED | CONVERGENCE | TWISTED (H | APPROXIMATION | Q)-BERNOULLI NUMBERS | Studies | Binomial distribution | Polynomials | Numerical analysis | Derivatives | Computer graphics

Journal Article

The Ramanujan Journal, ISSN 1382-4090, 5/2018, Volume 46, Issue 1, pp. 103 - 117

In this note, we shall obtain two closed forms for the Apostol–Bernoulli polynomials.

Fourier Analysis | Functions of a Complex Variable | Apostol–Bernoulli polynomials | Field Theory and Polynomials | Closed forms | 05A19 | Mathematics | Number Theory | Combinatorics | Stirling numbers | 11B68 | MATHEMATICS | FOURIER EXPANSIONS | HIGHER-ORDER | EULER POLYNOMIALS | GENOCCHI POLYNOMIALS | Q-EXTENSIONS | INTEGRAL-REPRESENTATIONS | FORMULAS | Apostol-Bernoulli polynomials | SUMS

Fourier Analysis | Functions of a Complex Variable | Apostol–Bernoulli polynomials | Field Theory and Polynomials | Closed forms | 05A19 | Mathematics | Number Theory | Combinatorics | Stirling numbers | 11B68 | MATHEMATICS | FOURIER EXPANSIONS | HIGHER-ORDER | EULER POLYNOMIALS | GENOCCHI POLYNOMIALS | Q-EXTENSIONS | INTEGRAL-REPRESENTATIONS | FORMULAS | Apostol-Bernoulli polynomials | SUMS

Journal Article

International Journal of Number Theory, ISSN 1793-0421, 08/2016, Volume 12, Issue 5, pp. 1259 - 1271

Let p > 3 be a prime, and let a be a rational p -adic integer. Let { B n } and { B n ( x ) } denote the Bernoulli numbers and Bernoulli polynomials given by B 0...

Euler number | Bernoulli polynomial | Congruence | MATHEMATICS | SEQUENCE | CONGRUENCES INVOLVING BERNOULLI | EULER NUMBERS

Euler number | Bernoulli polynomial | Congruence | MATHEMATICS | SEQUENCE | CONGRUENCES INVOLVING BERNOULLI | EULER NUMBERS

Journal Article

Advances in difference equations, ISSN 1687-1847, 2014, Volume 2014, Issue 1, pp. 1 - 9

We consider the Witt-type formula for the nth twisted Daehee numbers and polynomials and investigate some properties of those numbers and polynomials...

Bernoulli numbers of the second kind | Ordinary Differential Equations | Functional Analysis | Analysis | higher-order Bernoulli numbers | Difference and Functional Equations | Mathematics, general | Mathematics | Partial Differential Equations | the n th twisted Daehee numbers and polynomials | Higher-order Bernoulli numbers | The nth twisted Daehee numbers and polynomials | MATHEMATICS | MATHEMATICS, APPLIED | the nth twisted Daehee numbers and polynomials | Usage | Polynomials | Number theory | Difference equations | Formulas (mathematics)

Bernoulli numbers of the second kind | Ordinary Differential Equations | Functional Analysis | Analysis | higher-order Bernoulli numbers | Difference and Functional Equations | Mathematics, general | Mathematics | Partial Differential Equations | the n th twisted Daehee numbers and polynomials | Higher-order Bernoulli numbers | The nth twisted Daehee numbers and polynomials | MATHEMATICS | MATHEMATICS, APPLIED | the nth twisted Daehee numbers and polynomials | Usage | Polynomials | Number theory | Difference equations | Formulas (mathematics)

Journal Article

Mediterranean Journal of Mathematics, ISSN 1660-5446, 7/2015, Volume 12, Issue 3, pp. 679 - 695

In this paper, we introduce a new class of generalized Hermite–Bernoulli polynomials and derive some implicit summation formulae and symmetric identities by applying the generating functions...

33C45 | Hermite–Bernoulli polynomials | summation formulae | 33C99 | Mathematics, general | Mathematics | Bernoulli polynomials | Hermite polynomials | symmetric identities | MATHEMATICS | MATHEMATICS, APPLIED | Hermite-Bernoulli polynomials

33C45 | Hermite–Bernoulli polynomials | summation formulae | 33C99 | Mathematics, general | Mathematics | Bernoulli polynomials | Hermite polynomials | symmetric identities | MATHEMATICS | MATHEMATICS, APPLIED | Hermite-Bernoulli polynomials

Journal Article

Integral Transforms and Special Functions, ISSN 1065-2469, 08/2014, Volume 25, Issue 8, pp. 627 - 633

Boole polynomials play an important role in the area of number theory, algebra and umbral calculus...

Fermionic p-adic integral | Boole polynomials | integral transforms | Euler polynomials | MATHEMATICS | MATHEMATICS, APPLIED | BERNOULLI | Integral transforms | Functions (mathematics) | Algebra | Integrals | Mathematical analysis | Transforms | Calculus | Polynomials | Number theory

Fermionic p-adic integral | Boole polynomials | integral transforms | Euler polynomials | MATHEMATICS | MATHEMATICS, APPLIED | BERNOULLI | Integral transforms | Functions (mathematics) | Algebra | Integrals | Mathematical analysis | Transforms | Calculus | Polynomials | Number theory

Journal Article

15.
Full Text
A note on the values of weighted q-Bernstein polynomials and weighted q-Genocchi numbers

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

The rapid development of q-calculus has led to the discovery of new generalizations of Bernstein polynomials and Genocchi polynomials involving q-integers...

q -Bernstein polynomials | weighted q -Genocchi numbers and polynomials | 05A10 | 11B65 | Mathematics | 11B68 | Bernstein polynomials | weighted q -Bernstein polynomials | Ordinary Differential Equations | Functional Analysis | Genocchi numbers and polynomials | Analysis | 11B73 | Difference and Functional Equations | Mathematics, general | q -Genocchi numbers and polynomials | Partial Differential Equations | q-Genocchi numbers and polynomials | weighted q-Genocchi numbers and polynomials | q-Bernstein polynomials | weighted q-Bernstein polynomials | MATHEMATICS | MATHEMATICS, APPLIED | IDENTITIES | EULER POLYNOMIALS | BERNOULLI | Polynomials | Integral equations | Weighting (Statistics) | Functions (mathematics) | Difference equations | Integrals | Mathematical analysis | Texts | Representations | Combinatorial analysis

q -Bernstein polynomials | weighted q -Genocchi numbers and polynomials | 05A10 | 11B65 | Mathematics | 11B68 | Bernstein polynomials | weighted q -Bernstein polynomials | Ordinary Differential Equations | Functional Analysis | Genocchi numbers and polynomials | Analysis | 11B73 | Difference and Functional Equations | Mathematics, general | q -Genocchi numbers and polynomials | Partial Differential Equations | q-Genocchi numbers and polynomials | weighted q-Genocchi numbers and polynomials | q-Bernstein polynomials | weighted q-Bernstein polynomials | MATHEMATICS | MATHEMATICS, APPLIED | IDENTITIES | EULER POLYNOMIALS | BERNOULLI | Polynomials | Integral equations | Weighting (Statistics) | Functions (mathematics) | Difference equations | Integrals | Mathematical analysis | Texts | Representations | Combinatorial analysis

Journal Article

Journal of mathematical analysis and applications, ISSN 0022-247X, 2019, Volume 476, Issue 2, pp. 569 - 584

We show that each member of a doubly infinite sequence of highly nonlinear expressions of Bernoulli polynomials, which can be seen as linear combinations of certain higher-order convolutions...

Bernoulli polynomials | Eulerian polynomials | Bernoulli numbers | Convolution identities | MATHEMATICS | MATHEMATICS, APPLIED | Probability | Mathematics

Bernoulli polynomials | Eulerian polynomials | Bernoulli numbers | Convolution identities | MATHEMATICS | MATHEMATICS, APPLIED | Probability | Mathematics

Journal Article

International Journal of Number Theory, ISSN 1793-0421, 03/2018, Volume 14, Issue 2, pp. 595 - 613

We relate geometric polynomials and [Formula: see text]-Bernoulli polynomials with an integral representation, then obtain several properties of [Formula: see text...

finite summation | p-Bernoulli polynomial | Bernoulli polynomial | geometric polynomial | poly-Bernoulli polynomial

finite summation | p-Bernoulli polynomial | Bernoulli polynomial | geometric polynomial | poly-Bernoulli polynomial

Journal Article

Advances in Difference Equations, ISSN 1687-1839, 12/2015, Volume 2015, Issue 1, pp. 1 - 10

The degenerate Bernoulli polynomials were introduced by Carlitz and rediscovered later by Ustiniv under the name of Korobov polynomials of the second kind (see Carlitz in Arch. Math. (Basel) 7:28-33, 1956; Util. Math. 15:51-88, 1979...

05A30 | Mathematics | 11B68 | q -analogs of degenerate Bernoulli polynomials of the second kind | q -analogs of λ -Daehee polynomials | Ordinary Differential Equations | Functional Analysis | 11B83 | Analysis | Difference and Functional Equations | Mathematics, general | 05A19 | q -analogs of degenerate Bernoulli polynomials | Partial Differential Equations | q-analogs of degenerate Bernoulli polynomials of the second kind | q-analogs of λ-Daehee polynomials | q-analogs of degenerate Bernoulli polynomials | MATHEMATICS | MATHEMATICS, APPLIED | IDENTITIES | q-analogs of lambda-Daehee polynomials | Usage | Polynomials | Formulae | Names | Difference equations | Arches | Formulas (mathematics)

05A30 | Mathematics | 11B68 | q -analogs of degenerate Bernoulli polynomials of the second kind | q -analogs of λ -Daehee polynomials | Ordinary Differential Equations | Functional Analysis | 11B83 | Analysis | Difference and Functional Equations | Mathematics, general | 05A19 | q -analogs of degenerate Bernoulli polynomials | Partial Differential Equations | q-analogs of degenerate Bernoulli polynomials of the second kind | q-analogs of λ-Daehee polynomials | q-analogs of degenerate Bernoulli polynomials | MATHEMATICS | MATHEMATICS, APPLIED | IDENTITIES | q-analogs of lambda-Daehee polynomials | Usage | Polynomials | Formulae | Names | Difference equations | Arches | Formulas (mathematics)

Journal Article

Integral Transforms and Special Functions, ISSN 1065-2469, 03/2017, Volume 28, Issue 3, pp. 212 - 222

We prove characterizations of Appell polynomials by means of symmetric property. For these polynomials, we establish a simple linear expression in terms of Bernoulli and Euler polynomials...

generating function | Bernoulli polynomials | Fourier expansions | Appell sequences | Euler polynomials | MATHEMATICS | MATHEMATICS, APPLIED | Polynomials | Functions (mathematics) | Integrals | Mathematical analysis | Transforms | Fourier analysis | Symmetry

generating function | Bernoulli polynomials | Fourier expansions | Appell sequences | Euler polynomials | MATHEMATICS | MATHEMATICS, APPLIED | Polynomials | Functions (mathematics) | Integrals | Mathematical analysis | Transforms | Fourier analysis | Symmetry

Journal Article

Journal of Applied Mathematics and Computing, ISSN 1598-5865, 10/2018, Volume 58, Issue 1, pp. 75 - 94

... problems by Müntz–Legendre polynomials Y. Ordokhani 1 · P. Rahimkhani 1,2 Received: 29 July 2017 / Published online: 11 September 2017 © Korean Society...

Computational Mathematics and Numerical Analysis | Fractional variational problems | Rayleigh–Ritz method | Mathematics | Theory of Computation | Numerical method | Caputo fractional derivative | 34A08 | Mathematics of Computing | Mathematical and Computational Engineering | 34K28 | Müntz–Legendre polynomials | 65L10 | Rayleigh-Ritz method | MATHEMATICS | OPERATIONAL MATRIX | MATHEMATICS, APPLIED | BERNOULLI WAVELETS | Muntz-Legendre polynomials | DIFFERENTIAL-EQUATIONS | FORMULATION | EULER-LAGRANGE EQUATIONS | Norms | Error detection | Ritz method | Iterative methods | Mathematical analysis | Fractional calculus

Computational Mathematics and Numerical Analysis | Fractional variational problems | Rayleigh–Ritz method | Mathematics | Theory of Computation | Numerical method | Caputo fractional derivative | 34A08 | Mathematics of Computing | Mathematical and Computational Engineering | 34K28 | Müntz–Legendre polynomials | 65L10 | Rayleigh-Ritz method | MATHEMATICS | OPERATIONAL MATRIX | MATHEMATICS, APPLIED | BERNOULLI WAVELETS | Muntz-Legendre polynomials | DIFFERENTIAL-EQUATIONS | FORMULATION | EULER-LAGRANGE EQUATIONS | Norms | Error detection | Ritz method | Iterative methods | Mathematical analysis | Fractional calculus

Journal Article

No results were found for your search.

Cannot display more than 1000 results, please narrow the terms of your search.