Journal of Functional Analysis, ISSN 0022-1236, 06/2019, Volume 276, Issue 12, pp. 3714 - 3766

The aim of this paper is to develop foundations of umbral calculus on the space D′ of distributions on Rd, which leads to a general theory of Sheffer...

Umbral calculus on [formula omitted] | Polynomial sequence of binomial type on [formula omitted] | Shift-invariant operators | Sheffer sequence on [formula omitted] | GAMMA | MATHEMATICS | Polynomial sequence of binomial type on D | POISSON | Sheffer sequence on D | HARMONIC-ANALYSIS | Umbral calculus on D | APPELL POLYNOMIALS | Mathematics - Functional Analysis

Umbral calculus on [formula omitted] | Polynomial sequence of binomial type on [formula omitted] | Shift-invariant operators | Sheffer sequence on [formula omitted] | GAMMA | MATHEMATICS | Polynomial sequence of binomial type on D | POISSON | Sheffer sequence on D | HARMONIC-ANALYSIS | Umbral calculus on D | APPELL POLYNOMIALS | Mathematics - Functional Analysis

Journal Article

Journal of Pure and Applied Algebra, ISSN 0022-4049, 03/2020, Volume 224, Issue 3, pp. 958 - 986

The aim of the paper is to show the existence of some ingredients for an umbral calculus on some Ore extensions, in a manner analogous to Rota's classical...

Pincherle calculus | Coalgebra | Umbral calculus | Translation operators | Difference algebra | Ore extensions | MATHEMATICS | MATHEMATICS, APPLIED | Algebra

Pincherle calculus | Coalgebra | Umbral calculus | Translation operators | Difference algebra | Ore extensions | MATHEMATICS | MATHEMATICS, APPLIED | Algebra

Journal Article

中国科学：数学英文版, ISSN 1674-7283, 2014, Volume 57, Issue 9, pp. 1867 - 1874

In this paper,we investigate some properties of q-Bernoulli polynomials arising from q-umbral calculus.We find a formula for expressing any polynomial as a...

积分 | Bernoulli多项式 | 本影 | 线性组合 | 05A30 | 05A40 | q -Bernoulli polynomial | Mathematics | Applications of Mathematics | 11B68 | q -umbral calculus | q-Bernoulli polynomial | q-umbral calculus | Q-EULER POLYNOMIALS | INTEGRALS | MATHEMATICS | MATHEMATICS, APPLIED | NUMBERS | IDENTITIES | Calculus | Polynomials | Mathematical analysis | Joints | China

积分 | Bernoulli多项式 | 本影 | 线性组合 | 05A30 | 05A40 | q -Bernoulli polynomial | Mathematics | Applications of Mathematics | 11B68 | q -umbral calculus | q-Bernoulli polynomial | q-umbral calculus | Q-EULER POLYNOMIALS | INTEGRALS | MATHEMATICS | MATHEMATICS, APPLIED | NUMBERS | IDENTITIES | Calculus | Polynomials | Mathematical analysis | Joints | China

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 05/2014, Volume 233, pp. 599 - 607

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...

Appell sequence | Fermionic p-adic integral on [formula omitted] | Formal power series | Genocchi numbers and polynomials | Sheffer sequence | MATHEMATICS, APPLIED | Fermionic p-adic integral on Z(p) | BERNOULLI

Appell sequence | Fermionic p-adic integral on [formula omitted] | Formal power series | Genocchi numbers and polynomials | Sheffer sequence | MATHEMATICS, APPLIED | Fermionic p-adic integral on Z(p) | BERNOULLI

Journal Article

ADVANCES IN DIFFERENCE EQUATIONS, ISSN 1687-1847, 05/2019, Volume 2019, Issue 1, pp. 1 - 17

Recently, extended r-central factorial numbers of the second kind and extended r-central Bell polynomials were introduced and various results of them were...

MATHEMATICS | MATHEMATICS, APPLIED | Umbral calculus | 11B83 | Extended r-central factorial numbers of the second kind | 05A40 | 11B73 | 05A19 | Extended r-central Bell polynomials | Polynomials | Combinatorial analysis

MATHEMATICS | MATHEMATICS, APPLIED | Umbral calculus | 11B83 | Extended r-central factorial numbers of the second kind | 05A40 | 11B73 | 05A19 | Extended r-central Bell polynomials | Polynomials | Combinatorial analysis

Journal Article

Computer Aided Geometric Design, ISSN 0167-8396, 11/2015, Volume 39, pp. 1 - 16

The investigation of the umbral calculus based generalization of Bernstein polynomials and Bézier curves is continued in this paper: First a generalization of...

Umbral calculus | Bézier curve | de Casteljau algorithm | Bernstein polynomial | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | Bezier curve | Algorithms

Umbral calculus | Bézier curve | de Casteljau algorithm | Bernstein polynomial | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | Bezier curve | Algorithms

Journal Article

Computer Aided Geometric Design, ISSN 0167-8396, 08/2016, Volume 46, pp. 43 - 63

The investigation of a¯-Bernstein polynomials and a¯-Bézier curves is continued in this paper. It is shown that convolution of the parameters a¯=(a¯1,…,a¯n) is...

Umbral calculus | Bézier curve | Blossoming | Bernstein polynomial | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | Bezier curve | Algorithms

Umbral calculus | Bézier curve | Blossoming | Bernstein polynomial | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | Bezier curve | Algorithms

Journal Article

Journal of Computational Analysis and Applications, ISSN 1521-1398, 06/2019, Volume 26, Issue 6, pp. 1014 - 1031

Journal Article

Journal of Computational Analysis and Applications, ISSN 1521-1398, 07/2019, Volume 26, Issue 8, pp. 1504 - 1520

Journal Article

Journal of Number Theory, ISSN 0022-314X, 02/2015, Volume 147, pp. 871 - 882

Recently, R. Dere and Y. Simsek have studied applications of umbral algebra to generating functions for the Hermite type Genocchi polynomials and numbers [6]....

Linear functional | Bernoulli polynomials | Umbral calculus | MATHEMATICS | EULER POLYNOMIALS | Algebra

Linear functional | Bernoulli polynomials | Umbral calculus | MATHEMATICS | EULER POLYNOMIALS | Algebra

Journal Article

Journal of Computational Analysis and Applications, ISSN 1521-1398, 07/2019, Volume 27, Issue 1, pp. 173 - 188

Journal Article

12.
Full Text
On a generalization of Bernstein polynomials and Bézier curves based on umbral calculus

Computer Aided Geometric Design, ISSN 0167-8396, 06/2014, Volume 31, Issue 5, pp. 227 - 244

In Winkel (2001) a generalization of Bernstein polynomials and Bézier curves based on umbral calculus has been introduced. In the present paper we describe new...

Efficient evaluation | Interpolation | Generalized Bernstein polynomial | Umbral calculus | Generalized de Casteljau algorithm | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | Algorithms | Mathematical analysis | Bezier | Calculus | Polynomials | Criteria | Computer aided design | Polygons

Efficient evaluation | Interpolation | Generalized Bernstein polynomial | Umbral calculus | Generalized de Casteljau algorithm | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | Algorithms | Mathematical analysis | Bezier | Calculus | Polynomials | Criteria | Computer aided design | Polygons

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2015, Volume 2015, Issue 1, pp. 1 - 13

In this paper, we consider the degenerate poly-Bernoulli polynomials. We present several explicit formulas and recurrence relations for these polynomials....

11B83 | 05A40 | Analysis | umbral calculus | Mathematics, general | 05A19 | Mathematics | Applications of Mathematics | degenerate poly-Bernoulli polynomials | MATHEMATICS | MATHEMATICS, APPLIED | BERNSTEIN | Calculus | Polynomials | Mathematical analysis | Inequalities

11B83 | 05A40 | Analysis | umbral calculus | Mathematics, general | 05A19 | Mathematics | Applications of Mathematics | degenerate poly-Bernoulli polynomials | MATHEMATICS | MATHEMATICS, APPLIED | BERNSTEIN | Calculus | Polynomials | Mathematical analysis | Inequalities

Journal Article

Ars Combinatoria, ISSN 0381-7032, 07/2011, Volume 101, pp. 257 - 264

In this paper, we study invariant sequences by umbral method, and give some identities which are similar with the identities of Bernoulli numbers.

Bernoulli numbers | Invariant sequences | Umbral calculus | MATHEMATICS

Bernoulli numbers | Invariant sequences | Umbral calculus | MATHEMATICS

Journal Article

Journal of Computational Analysis and Applications, ISSN 1521-1398, 2017, Volume 22, Issue 5, pp. 831 - 840

In this paper, we introduce new degenerate Bernoulli polynomials which are derived from umbral calculus and investigate some interesting properties of those...

Degenerate bernoulli polynomial | Umbral calculus | Higher-order degenerate bernoulli polynomial | Degenerate Bernoulli polynomial | COMPUTER SCIENCE, THEORY & METHODS | Higher-order degenerate Bernoulli polynomial

Degenerate bernoulli polynomial | Umbral calculus | Higher-order degenerate bernoulli polynomial | Degenerate Bernoulli polynomial | COMPUTER SCIENCE, THEORY & METHODS | Higher-order degenerate Bernoulli polynomial

Journal Article

Advances in Difference Equations, ISSN 1687-1839, 12/2013, Volume 2013, Issue 1, pp. 1 - 7

In this paper, by using the orthogonality type as defined in the umbral calculus, we derive an explicit formula for several well-known polynomials as a linear...

Frobenius-Euler polynomial | Ordinary Differential Equations | Functional Analysis | Euler polynomial | Analysis | umbral calculus | Difference and Functional Equations | Mathematics, general | Mathematics | Bernoulli polynomial | Bessel polynomial | Partial Differential Equations | Umbral calculus | MATHEMATICS | MATHEMATICS, APPLIED | SYMMETRY | IDENTITIES | BERNOULLI | Z(P) | Usage | Polynomials | Functions, Orthogonal

Frobenius-Euler polynomial | Ordinary Differential Equations | Functional Analysis | Euler polynomial | Analysis | umbral calculus | Difference and Functional Equations | Mathematics, general | Mathematics | Bernoulli polynomial | Bessel polynomial | Partial Differential Equations | Umbral calculus | MATHEMATICS | MATHEMATICS, APPLIED | SYMMETRY | IDENTITIES | BERNOULLI | Z(P) | Usage | Polynomials | Functions, Orthogonal

Journal Article

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, 1/2020, Volume 114, Issue 1, pp. 1 - 19

Extended degenerate r-central factorial numbers of the second kind and extended degenerate r-central Bell polynomials were introduced recently, as a degenerate...

Umbral calculus | 11B83 | 05A40 | Theoretical, Mathematical and Computational Physics | 11B73 | Extended degenerate r -central Bell polynomials | Mathematics, general | Extended degenerate r -central factorial numbers of the second kind | 05A19 | Mathematics | Applications of Mathematics | Polynomials | Combinatorial analysis

Umbral calculus | 11B83 | 05A40 | Theoretical, Mathematical and Computational Physics | 11B73 | Extended degenerate r -central Bell polynomials | Mathematics, general | Extended degenerate r -central factorial numbers of the second kind | 05A19 | Mathematics | Applications of Mathematics | Polynomials | Combinatorial analysis

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2014, Volume 2014, Issue 1, pp. 1 - 16

In this paper, we consider the Barnes-type Peters polynomials. We present several explicit formulas and recurrence relations for these polynomials. Also, we...

Mathematics, general | Mathematics | Applications of Mathematics | Analysis | umbral calculus | Barnes-type Peters polynomials | MATHEMATICS | MATHEMATICS, APPLIED | DIFFERENTIAL POLYNOMIALS | Calculus | Polynomials | Mathematical analysis | Inequalities

Mathematics, general | Mathematics | Applications of Mathematics | Analysis | umbral calculus | Barnes-type Peters polynomials | MATHEMATICS | MATHEMATICS, APPLIED | DIFFERENTIAL POLYNOMIALS | Calculus | Polynomials | Mathematical analysis | Inequalities

Journal Article

Advances in Difference Equations, ISSN 1687-1839, 12/2015, Volume 2015, Issue 1, pp. 1 - 13

Poly-Bernoulli polynomials of the second kind were introduced in Kim et al. (Adv. Differ. Equ. 2014:219, 2014) as a generalization of the Bernoulli polynomial...

Ordinary Differential Equations | Functional Analysis | Analysis | umbral calculus | Difference and Functional Equations | poly-Bernoulli polynomials | Mathematics, general | Mathematics | Bernoulli polynomials | Stirling numbers | Partial Differential Equations | MATHEMATICS | MATHEMATICS, APPLIED | Evaluation | Usage | Polynomials | Calculus | Quantum theory | Difference equations | Mathematical analysis

Ordinary Differential Equations | Functional Analysis | Analysis | umbral calculus | Difference and Functional Equations | poly-Bernoulli polynomials | Mathematics, general | Mathematics | Bernoulli polynomials | Stirling numbers | Partial Differential Equations | MATHEMATICS | MATHEMATICS, APPLIED | Evaluation | Usage | Polynomials | Calculus | Quantum theory | Difference equations | Mathematical analysis

Journal Article

Results in Mathematics, ISSN 1422-6383, 6/2014, Volume 65, Issue 3, pp. 415 - 428

In this paper, we are concerned with establishing some new elements of q-harmonic analysis. Namely, we prove a generalized q-Paley-Wiener theorem. As a...

Mathematics | 30D15 | 46F12 | Convolution | 39A13 | 47A16 | 44A35 | Paley-Wiener theorem | 33D60 | entire functions | q -analogues | Mathematics, general | hypercyclic and chaotic operators | q-analogues | UMBRAL CALCULUS | MATHEMATICS | MATHEMATICS, APPLIED | CHAOTIC CONVOLUTION-OPERATORS

Mathematics | 30D15 | 46F12 | Convolution | 39A13 | 47A16 | 44A35 | Paley-Wiener theorem | 33D60 | entire functions | q -analogues | Mathematics, general | hypercyclic and chaotic operators | q-analogues | UMBRAL CALCULUS | MATHEMATICS | MATHEMATICS, APPLIED | CHAOTIC CONVOLUTION-OPERATORS

Journal Article

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