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

Research output: Journal ArticleArticlepeer-review


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 languageAmerican English
JournalScience China Mathematics
StatePublished - 0015


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


  • Physical Sciences and Mathematics
  • Applied Mathematics

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