Integrals and iterated integrals and Borwein-Chen-Dilcher polynomials Articles uri icon

publication date

  • October 2020

start page

  • 1

end page

  • 19

issue

  • 5

volume

  • 17

International Standard Serial Number (ISSN)

  • 1660-5446

Electronic International Standard Serial Number (EISSN)

  • 1660-5454

abstract

  • We study the zero location and the asymptotic behavior of iterated integrals of polynomials. Borwein–Chen–Dilcher"s polynomials play an important role in this issue. For these polynomials we find their strong asymptotics and give the limit measure of their zero distribution. We apply these results to describe the zero asymptotic distribution of iterated integrals of ultraspherical polynomials with parameters (2α+1)/2, α∈Z+.

keywords

  • asymptotic behaviour; iterated integrals; orthogonal polynomials; zeros of polynomials