On extreme zeros of classical orthogonal polynomials

Ilia Krasikov*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Let x1 and xk be the least and the largest zeros of the Laguerre or Jacobi polynomial of degree k. We shall establish sharp inequalities of the form x1 < A, xk > B, which are uniform in all the parameters involved. Together with inequalities in the opposite direction, recently obtained by the author, this locates the extreme zeros of classical orthogonal polynomials with a high precision.

Original languageEnglish
Pages (from-to)168-182
Number of pages15
JournalJournal of Computational and Applied Mathematics
Issue number1
StatePublished - 15 Aug 2006
Externally publishedYes


  • Jacobi polynomials
  • Laguerre polynomials
  • Orthogonal polynomials
  • Zeros


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