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Articles 302581 - 302581 of 302581
Full-Text Articles in Physical Sciences and Mathematics
The Pascal Matrix Function And Its Applications To Bernoulli Numbers And Bernoulli Polynomials And Euler Numbers And Euler Polynomials, Tian-Xiao He, Jeff Liao, Peter Shiue
The Pascal Matrix Function And Its Applications To Bernoulli Numbers And Bernoulli Polynomials And Euler Numbers And Euler Polynomials, Tian-Xiao He, Jeff Liao, Peter Shiue
Tian-Xiao He
A Pascal matrix function is introduced by Call and Velleman in [3]. In this paper, we will use the function to give a uni#12;ed 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.