Linear Algebra and Its Applications, ISSN 0024-3795, 2011, Volume 434, Issue 10, pp. 2187 - 2196

Let Ω m , n ( α , β , γ ) denote a set of all elements of weighted lattice paths with weight ( α , β , γ ) in the xy-plane from ( 0 , 0 ) to ( m , n ) such...

Weighted lattice path | Lattice path matrix | Positive definite | LDU decomposition | Generalized Pascal matrix | MATHEMATICS, APPLIED

Weighted lattice path | Lattice path matrix | Positive definite | LDU decomposition | Generalized Pascal matrix | MATHEMATICS, APPLIED

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 2007, Volume 423, Issue 2, pp. 230 - 245

In this paper, we introduce the generalized Pascal functional matrix and show that the existing variations of Pascal matrices are special cases of this...

Generalizing functions | Generalized Pascal functional matrix | Combinatorial identities | LU decomposition | Pascal matrices | MATHEMATICS, APPLIED | LINEAR ALGEBRA | ALGEBRAIC PROPERTIES | generalized Pascal functional matrix | combinatorial identities | generalizing functions

Generalizing functions | Generalized Pascal functional matrix | Combinatorial identities | LU decomposition | Pascal matrices | MATHEMATICS, APPLIED | LINEAR ALGEBRA | ALGEBRAIC PROPERTIES | generalized Pascal functional matrix | combinatorial identities | generalizing functions

Journal Article

Communications in Statistics - Theory and Methods, ISSN 0361-0926, 07/2015, Volume 44, Issue 13, pp. 2738 - 2752

This article defines the so called Generalized Matrix Variate Jensen-Logistic distribution. The relevant applications of this class of distributions in...

Statistical shape theory | 05A99 | 33E99 | Jensen-Logistic distribution | Generalized Kummer relations | 02E15 | Pascal triangle | Zonal polynomials | SHAPE | ARGUMENTS | STATISTICAL-THEORY | STATISTICS & PROBABILITY | ELLIPTIC MODELS | INVARIANT POLYNOMIALS | PASCAL | Logistics | Pascal (programming language) | Mathematical analysis | Triangles | Mathematical models | Polynomials | Derivatives | Computational efficiency | Density

Statistical shape theory | 05A99 | 33E99 | Jensen-Logistic distribution | Generalized Kummer relations | 02E15 | Pascal triangle | Zonal polynomials | SHAPE | ARGUMENTS | STATISTICAL-THEORY | STATISTICS & PROBABILITY | ELLIPTIC MODELS | INVARIANT POLYNOMIALS | PASCAL | Logistics | Pascal (programming language) | Mathematical analysis | Triangles | Mathematical models | Polynomials | Derivatives | Computational efficiency | Density

Journal Article

LINEAR ALGEBRA AND ITS APPLICATIONS, ISSN 0024-3795, 09/2019, Volume 577, pp. 214 - 239

Let B-n = [B-n,B-k](n,k)>= 0 be the Bell matrix. Define the n x n shift Bell matrix P-n,P-k by (P-n,P-k)(i,j) = B-k+i-1,B-kj-1 for j = 1, 2, ... n and k = 0,...

MATHEMATICS | MATHEMATICS, APPLIED | IDENTITIES | NUMBERS | Bell polynomials | Generalized Riordan array | TRIANGLES | n x n shift iteration matrix | GENERALIZED PASCAL MATRIX | n x n shift Bell matrix

MATHEMATICS | MATHEMATICS, APPLIED | IDENTITIES | NUMBERS | Bell polynomials | Generalized Riordan array | TRIANGLES | n x n shift iteration matrix | GENERALIZED PASCAL MATRIX | n x n shift Bell matrix

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 02/2017, Volume 446, Issue 1, pp. 87 - 100

This paper deals with a unified matrix representation for the Sheffer polynomials. The core of the proposed approach is the so-called creation matrix, a...

Binomial type polynomials | Generalized Pascal matrix | Sheffer polynomials | Appell polynomials | Creation matrix | MATHEMATICS | DETERMINANTAL APPROACH | MATHEMATICS, APPLIED | BELL POLYNOMIALS | SEQUENCES | IDENTITIES

Binomial type polynomials | Generalized Pascal matrix | Sheffer polynomials | Appell polynomials | Creation matrix | MATHEMATICS | DETERMINANTAL APPROACH | MATHEMATICS, APPLIED | BELL POLYNOMIALS | SEQUENCES | IDENTITIES

Journal Article

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), ISSN 0302-9743, 2017, Volume 10405, pp. 409 - 421

Conference Proceeding

Electronic Journal of Linear Algebra, ISSN 1081-3810, 01/2009, Volume 18, pp. 564 - 588

The purpose of this article is to study determinants of matrices which are known as generalized Pascal triangles (see R. Bacher. Determinants of matrices...

Fibonacci (lucas | Generalized pascal triangle | Determinant | Generalized symmetric (skymmetric) pascal triangle | Catalan) sequence | Matrix factorization | Recursive relation | Toeplitz matrix | Golden ratio | Fibonacci (Lucas, Catalan) sequence | MATHEMATICS | FIBONACCI | Generalized symmetric (skymmetric) Pascal triangle | LUCAS-NUMBERS | Generalized Pascal triangle

Fibonacci (lucas | Generalized pascal triangle | Determinant | Generalized symmetric (skymmetric) pascal triangle | Catalan) sequence | Matrix factorization | Recursive relation | Toeplitz matrix | Golden ratio | Fibonacci (Lucas, Catalan) sequence | MATHEMATICS | FIBONACCI | Generalized symmetric (skymmetric) Pascal triangle | LUCAS-NUMBERS | Generalized Pascal triangle

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 2009, Volume 225, Issue 1, pp. 309 - 315

In this paper, we give an algorithm for solving linear systems of the Pascal matrices. The method is based on the explicit factorization of the Pascal...

Pascal matrix | Generalized Pascal matrix | Toeplitz matrix | Factorization | Algorithm | Linear systems | Algorithms

Pascal matrix | Generalized Pascal matrix | Toeplitz matrix | Factorization | Algorithm | Linear systems | Algorithms

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 02/2015, Volume 253, pp. 83 - 101

A simple but elegant method was adopted in Youn and Yang (2011) in order to derive a differential equation and recursive formulas for Sheffer polynomials....

Generalized Pascal functional matrix | Umbral calculus | Wronskian matrix | Sheffer sequences | MATHEMATICS, APPLIED | NUMBERS

Generalized Pascal functional matrix | Umbral calculus | Wronskian matrix | Sheffer sequences | MATHEMATICS, APPLIED | NUMBERS

Journal Article

International Journal of Computer Mathematics, ISSN 0020-7160, 10/2016, Volume 93, Issue 10, pp. 1756 - 1770

Let s be arbitrary integer, we introduce the notion of the matrix of type s, whose nonzero entries are the classical Horadam numbers . In this paper we...

11B39 | generalized Fibonacci number | generalized Pascal matrix | 05A10 | Moore-Penrose inverse | Horadam number | 15A09 | generalized Fibonacci matrix | Moore–Penrose inverse | MATHEMATICS, APPLIED | COMBINATORIAL IDENTITIES | NORMS | CIRCULANT MATRICES | LUCAS-NUMBERS | Computer science | Inverse problems | Integers | Pascal (programming language) | Correlation | Images | Mathematical models | Inverse | Combinatorial analysis

11B39 | generalized Fibonacci number | generalized Pascal matrix | 05A10 | Moore-Penrose inverse | Horadam number | 15A09 | generalized Fibonacci matrix | Moore–Penrose inverse | MATHEMATICS, APPLIED | COMBINATORIAL IDENTITIES | NORMS | CIRCULANT MATRICES | LUCAS-NUMBERS | Computer science | Inverse problems | Integers | Pascal (programming language) | Correlation | Images | Mathematical models | Inverse | Combinatorial analysis

Journal Article

Mediterranean Journal of Mathematics, ISSN 1660-5446, 10/2019, Volume 16, Issue 5, pp. 1 - 20

In this contribution, some new identities involving Sheffer–Appell polynomial sequences using generalized Pascal functional and Wronskian matrices are deduced....

33C45 | identities | 15A24 | generalized Pascal functional | Mathematics, general | Mathematics | Wronskian matrices | 15A15 | Sheffer–Appell polynomial sequence | orthogonal polynomials | MATHEMATICS | DETERMINANTAL APPROACH | MATHEMATICS, APPLIED | APOSTOL-BERNOULLI | Sheffer-Appell polynomial sequence

33C45 | identities | 15A24 | generalized Pascal functional | Mathematics, general | Mathematics | Wronskian matrices | 15A15 | Sheffer–Appell polynomial sequence | orthogonal polynomials | MATHEMATICS | DETERMINANTAL APPROACH | MATHEMATICS, APPLIED | APOSTOL-BERNOULLI | Sheffer-Appell polynomial sequence

Journal Article

IEEE Transactions on Circuits and Systems I: Regular Papers, ISSN 1549-8328, 10/2008, Volume 55, Issue 9, pp. 2650 - 2663

This paper proposes a one-to-one mapping between the coefficients of continuous-time ( s -domain) and discrete-time ( z -domain) IIR transfer functions such...

Linear systems | first-order s - z transformation | Transfer functions | one-to-one coefficient mapping | Nonlinear filters | IIR filters | Closed-form solution | Information technology | Information science | continuous-time (CT) filter | Polynomials | Generalized Pascal matrix | discrete-time (DT) filter | inverse Pascal matrix | Continuous-time (CT) filter | Discrete-time (DT) filter | First-order s-z transformation | One-to-one coefficient mapping | Inverse Pascal matrix | first-order s-z transformation | ENGINEERING, ELECTRICAL & ELECTRONIC | Discrete-time systems | Evaluation | Mathematical analysis | Electric filters | Transformations (Mathematics) | Design and construction | Methods | Pascal (programming language) | Circuits | Mapping | Matrices | Transformations | Boundaries | Matrix methods

Linear systems | first-order s - z transformation | Transfer functions | one-to-one coefficient mapping | Nonlinear filters | IIR filters | Closed-form solution | Information technology | Information science | continuous-time (CT) filter | Polynomials | Generalized Pascal matrix | discrete-time (DT) filter | inverse Pascal matrix | Continuous-time (CT) filter | Discrete-time (DT) filter | First-order s-z transformation | One-to-one coefficient mapping | Inverse Pascal matrix | first-order s-z transformation | ENGINEERING, ELECTRICAL & ELECTRONIC | Discrete-time systems | Evaluation | Mathematical analysis | Electric filters | Transformations (Mathematics) | Design and construction | Methods | Pascal (programming language) | Circuits | Mapping | Matrices | Transformations | Boundaries | Matrix methods

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 03/2014, Volume 444, pp. 114 - 131

In this paper we establish plenty of number theoretic and combinatoric identities involving generalized Bernoulli polynomials and Stirling numbers of both...

Bernoulli matrix | Bernoulli polynomials | Pascal matrix | Stirling numbers | Hyperharmonic numbers | Stirling matrix | MATHEMATICS, APPLIED | DEGENERATE BERNOULLI | NUMBERS | POLYNOMIALS | LINEAR ALGEBRA | ALGEBRAIC PROPERTIES | GENERALIZED PASCAL MATRIX | FUNCTIONAL MATRIX | Mathematics - Number Theory

Bernoulli matrix | Bernoulli polynomials | Pascal matrix | Stirling numbers | Hyperharmonic numbers | Stirling matrix | MATHEMATICS, APPLIED | DEGENERATE BERNOULLI | NUMBERS | POLYNOMIALS | LINEAR ALGEBRA | ALGEBRAIC PROPERTIES | GENERALIZED PASCAL MATRIX | FUNCTIONAL MATRIX | Mathematics - Number Theory

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 08/2008, Volume 156, Issue 15, pp. 3040 - 3045

In this paper, we study the Jordan canonical form of the generalized Pascal functional matrix associated with a sequence of binomial type, and demonstrate that...

Sequence of binomial type | Generalized Pascal functional matrix | Bell polynomial | Jordan canonical form | Pascal matrix | Iteration matrix | Stirling number | MATHEMATICS, APPLIED | LINEAR ALGEBRA | STIRLING MATRIX | FUNCTIONAL MATRIX

Sequence of binomial type | Generalized Pascal functional matrix | Bell polynomial | Jordan canonical form | Pascal matrix | Iteration matrix | Stirling number | MATHEMATICS, APPLIED | LINEAR ALGEBRA | STIRLING MATRIX | FUNCTIONAL MATRIX

Journal Article

15.
Full Text
Identities for degenerate Bernoulli polynomials and Korobov polynomials of the first kind

Science China Mathematics, ISSN 1674-7283, 5/2019, 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. Then we apply twelve...

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

16.
Full Text
Some identities on Catalan numbers and hypergeometric functions via Catalan matrix power

Applied Mathematics and Computation, ISSN 0096-3003, 2011, Volume 217, Issue 22, pp. 9122 - 9132

In this paper we use the Catalan matrix power as a tool for deriving identities involving Catalan numbers and hypergeometric functions. For that purpose, we...

Catalan matrix power | Pascal matrix | Catalan numbers | Catalan matrix | Hypergeometric identities | Generalized hypergeometric function | MATHEMATICS, APPLIED | COMBINATORIAL IDENTITIES | FIBONACCI | Hypergeometric functions | Pascal (programming language) | Simplification | Computation | Mathematical analysis | Tools | Mathematical models

Catalan matrix power | Pascal matrix | Catalan numbers | Catalan matrix | Hypergeometric identities | Generalized hypergeometric function | MATHEMATICS, APPLIED | COMBINATORIAL IDENTITIES | FIBONACCI | Hypergeometric functions | Pascal (programming language) | Simplification | Computation | Mathematical analysis | Tools | Mathematical models

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 2009, Volume 215, Issue 2, pp. 796 - 805

We introduce the notion of the Catalan matrix C n [ x ] whose non-zero elements are expressions which contain the Catalan numbers arranged into a lower...

Pascal matrix | Combinatorial identities | Catalan numbers | Catalan matrix | Generalized hypergeometric function | Euler gamma function | MATHEMATICS, APPLIED | FIBONACCI

Pascal matrix | Combinatorial identities | Catalan numbers | Catalan matrix | Generalized hypergeometric function | Euler gamma function | MATHEMATICS, APPLIED | FIBONACCI

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 2008, Volume 156, Issue 14, pp. 2793 - 2803

In this paper, we study the relations between the Bell matrix and the Fibonacci matrix, which provide a unified approach to some lower triangular matrices,...

Generalized Fibonacci numbers | Combinatorial identities | Iteration matrix | Fibonacci numbers | Bell polynomials | POLYNOMIALS | MATHEMATICS, APPLIED | LINEAR ALGEBRA | GENERALIZED PASCAL MATRIX | STIRLING MATRIX

Generalized Fibonacci numbers | Combinatorial identities | Iteration matrix | Fibonacci numbers | Bell polynomials | POLYNOMIALS | MATHEMATICS, APPLIED | LINEAR ALGEBRA | GENERALIZED PASCAL MATRIX | STIRLING MATRIX

Journal Article

UTILITAS MATHEMATICA, ISSN 0315-3681, 09/2017, Volume 104, pp. 47 - 66

There are scattered results in the literature showing that the leading principal minors of certain infinite integer matrices form the Fibonacci and Lucas...

MATHEMATICS, APPLIED | Lucas sequence | Recurrence relation | Fibonacci sequence | Determinant | STATISTICS & PROBABILITY | Matrix factorization | Toeplitz matrix | Jacobsthal sequence | Generalized Pascal triangle | Pell sequence | 7-matrix | TOEPLITZ | FIBONACCI

MATHEMATICS, APPLIED | Lucas sequence | Recurrence relation | Fibonacci sequence | Determinant | STATISTICS & PROBABILITY | Matrix factorization | Toeplitz matrix | Jacobsthal sequence | Generalized Pascal triangle | Pell sequence | 7-matrix | TOEPLITZ | FIBONACCI

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 04/2015, Volume 471, pp. 569 - 574

In a recent article in this journal Deveci and Karaduman [3] proposed several conjectures (two of which have been proven by Hiller [4]) regarding the order of...

Order of cyclic groups | Integer matrices | Generalized Pascal matrices | Primes | MATHEMATICS | MATHEMATICS, APPLIED

Order of cyclic groups | Integer matrices | Generalized Pascal matrices | Primes | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

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