1.
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

2009, ISBN 9780195334548, xiv, 422

Like the intriguing Fibonacci and Lucas numbers, Catalan numbers are also ubiquitous. "They have the same delightful propensity for popping up unexpectedly,...

Catalan numbers (Mathematics) | Mathematics | Euler's triangulation problem | Pascal's triangle | Pascal's identity | Lucas numbers | Catalan sequence | Parenthesization problem | Catalan numbers | Martin gardner | Fibonacci numbers

Catalan numbers (Mathematics) | Mathematics | Euler's triangulation problem | Pascal's triangle | Pascal's identity | Lucas numbers | Catalan sequence | Parenthesization problem | Catalan numbers | Martin gardner | Fibonacci numbers

Book

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 | POLYNOMIALS | MATHEMATICS | MATHEMATICS, APPLIED | DEGENERATE BERNOULLI | LINEAR ALGEBRA | Mathematics - Number Theory

Bernoulli matrix | Bernoulli polynomials | Pascal matrix | Stirling numbers | Hyperharmonic numbers | Stirling matrix | POLYNOMIALS | MATHEMATICS | MATHEMATICS, APPLIED | DEGENERATE BERNOULLI | LINEAR ALGEBRA | Mathematics - Number Theory

Journal Article

Discrete Mathematics, ISSN 0012-365X, 2008, Volume 308, Issue 18, pp. 4246 - 4262

We consider an identity relating Fibonacci numbers to Pascal's triangle discovered by G.E. Andrews. Several authors provided proofs of this identity, most of...

Hypergeometric functions | Pascal's triangle | Identity of Andrews | Riordan array | Catalan's triangle | MATHEMATICS | hypergeometric functions | CATALAN NUMBERS | identity of Andrews | INVERSION | FORMULA | FIBONACCI NUMBERS | SUMS

Hypergeometric functions | Pascal's triangle | Identity of Andrews | Riordan array | Catalan's triangle | MATHEMATICS | hypergeometric functions | CATALAN NUMBERS | identity of Andrews | INVERSION | FORMULA | FIBONACCI NUMBERS | SUMS

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

6.
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Linear recurrences associated to rays in Pascal's triangle and combinatorial identities

Mathematica Slovaca, ISSN 0139-9918, 2014, Volume 64, Issue 2, pp. 287 - 300

Our main purpose is to describe the recurrence relation associated to the sum of diagonal elements laying along a finite ray crossing Pascal's triangle. We...

combinatorial properties | Pascal triangles | linear recurrences | POLYNOMIALS | MATHEMATICS | CHEBYSHEV | MORGAN-VOYCE | SUMS

combinatorial properties | Pascal triangles | linear recurrences | POLYNOMIALS | MATHEMATICS | CHEBYSHEV | MORGAN-VOYCE | SUMS

Journal Article

Discrete Mathematics, ISSN 0012-365X, 08/2012, Volume 312, Issue 15, pp. 2197 - 2202

We obtain explicit formulas that express the complete homogeneous symmetric polynomials of the sequence of partial sums sk of a sequence xk as polynomials in...

Legendre–Stirling numbers | Symmetric polynomials | Gaussian coefficients | Generalized Stirling numbers | [formula omitted]-Stirling numbers | q-Stirling numbers | Legendre-Stirling numbers | MATHEMATICS | DIVIDED DIFFERENCES | PASCAL MATRICES

Legendre–Stirling numbers | Symmetric polynomials | Gaussian coefficients | Generalized Stirling numbers | [formula omitted]-Stirling numbers | q-Stirling numbers | Legendre-Stirling numbers | MATHEMATICS | DIVIDED DIFFERENCES | PASCAL MATRICES

Journal Article

Indian Journal of Pure and Applied Mathematics, ISSN 0019-5588, 10/2007, Volume 38, Issue 5, pp. 457 - 465

In this paper, the Lucas matrix L-n is introduced. Let P-n[x] and Q(n)[x] be the generalized Pascal matrix of first and second kinds, which are defined in...

Pascal matrix | Combinatorial identity | Lucas matrix | Factorization of matrix | MATHEMATICS | factorization of matrix | combinatorial identity

Pascal matrix | Combinatorial identity | Lucas matrix | Factorization of matrix | MATHEMATICS | factorization of matrix | combinatorial identity

Journal Article

9.
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A global boundary integral equation method for recovering space–time dependent heat source

International Journal of Heat and Mass Transfer, ISSN 0017-9310, 01/2016, Volume 92, pp. 1034 - 1040

•A new meshless approach to tackle different inverse heat source problems accurately.•The novel scheme is applicable for inverse heat source problems with 10-1...

Adjoint Trefftz test functions | Green’s second identity | Reciprocity gap functional | Heat source recovery problem | Pascal polynomials | Green's second identity | CAUCHY-PROBLEM | IDENTIFICATION | ENGINEERING, MECHANICAL | NUMERICAL-SOLUTION | MECHANICS | CONDUCTION EQUATION | THERMODYNAMICS | TEMPERATURE | FUNDAMENTAL-SOLUTIONS

Adjoint Trefftz test functions | Green’s second identity | Reciprocity gap functional | Heat source recovery problem | Pascal polynomials | Green's second identity | CAUCHY-PROBLEM | IDENTIFICATION | ENGINEERING, MECHANICAL | NUMERICAL-SOLUTION | MECHANICS | CONDUCTION EQUATION | THERMODYNAMICS | TEMPERATURE | FUNDAMENTAL-SOLUTIONS

Journal Article

Theoretical Computer Science, ISSN 0304-3975, 07/2019, Volume 778, pp. 73 - 77

A bound resembling Pascal's identity is presented for binary necklaces with fixed density using Lyndon words with fixed density. The result is generalized to...

Necklaces | Lyndon word | Pascal's identity | Nichols algebras | Fixed-density | COMPUTER SCIENCE, THEORY & METHODS

Necklaces | Lyndon word | Pascal's identity | Nichols algebras | Fixed-density | COMPUTER SCIENCE, THEORY & METHODS

Journal Article

11.
Full Text
Linear recurrences associated to rays in Pascal’s triangle and combinatorial identities

Mathematica Slovaca, ISSN 0139-9918, 4/2014, Volume 64, Issue 2, pp. 287 - 300

Our main purpose is to describe the recurrence relation associated to the sum of diagonal elements laying along a finite ray crossing Pascal’s triangle. We...

Algebra | linear recurrences | Mathematics, general | Mathematics | Primary 11B39, 05A19, 11A55, 05A10, 11B65, 05A15 | combinatorial properties | Pascal triangles

Algebra | linear recurrences | Mathematics, general | Mathematics | Primary 11B39, 05A19, 11A55, 05A10, 11B65, 05A15 | combinatorial properties | Pascal triangles

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

Discrete Applied Mathematics, ISSN 0166-218X, 2003, Volume 130, Issue 3, pp. 527 - 534

The Pascal matrix and the Stirling matrices of the first kind and the second kind obtained from the Fibonacci matrix are studied, respectively. Also, we obtain...

Fibonacci matrix | Pascal matrix | Stirling matrix of the first kind | Stirling matrix of the second kind | MATHEMATICS, APPLIED | MATRICES

Fibonacci matrix | Pascal matrix | Stirling matrix of the first kind | Stirling matrix of the second kind | MATHEMATICS, APPLIED | MATRICES

Journal Article

Organon F, ISSN 1335-0668, 2018, Volume 25, Issue 2, pp. 196 - 214

In this paper, I try to argue that, from the methodological position of reflected equilibrium, it seems to be reasonable to build a theory of personal identity...

Epistemology | Philosophy of Science | Marya Schechtman | Reflected equilibrium | Afterlife | Pascal's wager | Life | Personal identity | Radim Belohrad | Samuel Scheffler | Person | IDENTITY | reflected equilibrium | afterlife | PHILOSOPHY | person-life | personal identity | Scheffler

Epistemology | Philosophy of Science | Marya Schechtman | Reflected equilibrium | Afterlife | Pascal's wager | Life | Personal identity | Radim Belohrad | Samuel Scheffler | Person | IDENTITY | reflected equilibrium | afterlife | PHILOSOPHY | person-life | personal identity | Scheffler

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

ACAROLOGIA, ISSN 0044-586X, 2019, Volume 59, Issue 2, pp. 261 - 278

The identity of Blaise Pascal's mite is examined. Linguistics, morphology, habitat and size reveal that Pascal's mite is not Acarus siro L., as usually...

Blaise Pascal | SCABIES | MEDICINE | CHEESE | Sarcoptes scabiei (L.) | Acarus siro L | ENTOMOLOGY | mite | ciron

Blaise Pascal | SCABIES | MEDICINE | CHEESE | Sarcoptes scabiei (L.) | Acarus siro L | ENTOMOLOGY | mite | ciron

Journal Article

1991, 1st Trinity Press International ed. --, ISBN 1563380048, 224

Book

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

Journal of Integer Sequences, 2015, Volume 18, Issue 5

Journal Article

Boletín de la Sociedad Matemática Mexicana, ISSN 1405-213X, 10/2016, Volume 22, Issue 2, pp. 329 - 335

Graph lattice has vertices at points with non-negative integer coordinates. From each vertex we have two edges: horizontal and vertical neighboring vertices...

Pascal’s triangle | Combinatorial identity | Random walks | The probability of transition | 05C63 Infinite graphs | Mathematics, general | Mathematics | Directed graph | Reachability of vertices | 05C81 Random walks on graphs | Pascal's triangle

Pascal’s triangle | Combinatorial identity | Random walks | The probability of transition | 05C63 Infinite graphs | Mathematics, general | Mathematics | Directed graph | Reachability of vertices | 05C81 Random walks on graphs | Pascal's triangle

Journal Article

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