Equioscillatory property of the Laguerre polynomials

Ilia Krasikov*, Alexander Zarkh

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We show that the function ((x-dm)(x-dM))1/4xα/2e-x/2Lk(α)(x) is almost equioscillating with the amplitude 2/π provided k and α are large enough. Here Lk(α)(x) is the orthonormal Laguerre polynomial of degree k and dm, dM are some approximations for the extreme zeros. As a corollary we obtain a very explicit, uniform in k and α, sharp upper bound on the Laguerre polynomials.

Original languageEnglish
Pages (from-to)2021-2047
Number of pages27
JournalJournal of Approximation Theory
Issue number11
StatePublished - Nov 2010
Externally publishedYes


  • Bounds
  • Inequalities
  • Laguerre polynomials
  • Orthogonal polynomials


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