The Pascal Matrix Function and Its Applications to Bernoulli Numbers and Bernoulli Polynomials and Euler Numbers and Euler Polynomials

Tian-Xiao He; Jeff H.C. Liao; Peter J.-S. Shiue

The Pascal Matrix Function and Its Applications to Bernoulli Numbers and Bernoulli Polynomials and Euler Numbers and Euler Polynomials

Tian-Xiao He, Jeff H.C. Liao, Peter J.-S. Shiue

Illinois Wesleyan University

Research output: Journal Article › Article › peer-review

Abstract

A Pascal matrix function is introduced by Call and Velleman in [3]. In this paper, we will use the function to give a unied approach in the study of Bernoulli numbers and Bernoulli polynomials. Many well-known and new properties of the Bernoulli numbers and polynomials can be established by using the Pascal matrix function. The approach is also applied to the study of Euler numbers and Euler polynomials.

Original language	American English
Journal	Science China Mathematics
Volume	45
State	Published - 0015

Keywords

Bernoulli number
Bernoulli polynomial
Euler number
Euler polynomial.
Pascal matrix
Pascal matrix func- tion

Disciplines

Physical Sciences and Mathematics
Applied Mathematics

Access to Document

pascal_matrix_function.pdfFinal published version, 264 KBLicense: Unspecified

Cite this

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title = "The Pascal Matrix Function and Its Applications to Bernoulli Numbers and Bernoulli Polynomials and Euler Numbers and Euler Polynomials",

abstract = " A Pascal matrix function is introduced by Call and Velleman in [3]. In this paper, we will use the function to give a unied approach in the study of Bernoulli numbers and Bernoulli polynomials. Many well-known and new properties of the Bernoulli numbers and polynomials can be established by using the Pascal matrix function. The approach is also applied to the study of Euler numbers and Euler polynomials.",

keywords = "Bernoulli number, Bernoulli polynomial, Euler number, Euler polynomial., Pascal matrix, Pascal matrix func- tion",

author = "Tian-Xiao He and Liao, {Jeff H.C.} and Shiue, {Peter J.-S.}",

year = "15",

language = "American English",

volume = "45",

journal = "Science China Mathematics",

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TY - JOUR

T1 - The Pascal Matrix Function and Its Applications to Bernoulli Numbers and Bernoulli Polynomials and Euler Numbers and Euler Polynomials

AU - He, Tian-Xiao

AU - Liao, Jeff H.C.

AU - Shiue, Peter J.-S.

PY - 15

Y1 - 15

N2 - A Pascal matrix function is introduced by Call and Velleman in [3]. In this paper, we will use the function to give a unied approach in the study of Bernoulli numbers and Bernoulli polynomials. Many well-known and new properties of the Bernoulli numbers and polynomials can be established by using the Pascal matrix function. The approach is also applied to the study of Euler numbers and Euler polynomials.

AB - A Pascal matrix function is introduced by Call and Velleman in [3]. In this paper, we will use the function to give a unied approach in the study of Bernoulli numbers and Bernoulli polynomials. Many well-known and new properties of the Bernoulli numbers and polynomials can be established by using the Pascal matrix function. The approach is also applied to the study of Euler numbers and Euler polynomials.

KW - Bernoulli number

KW - Bernoulli polynomial

KW - Euler number

KW - Euler polynomial.

KW - Pascal matrix

KW - Pascal matrix func- tion

M3 - Article

VL - 45

JO - Science China Mathematics

JF - Science China Mathematics

ER -