Asymptotic Properties of Zeros of Hypergeometric Polynomials

Peter L. Duren, Bertrand J. Guillou

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


In a paper by K. Driver and P. Duren (1999, Numer. Algorithms21, 147-156) a theorem of Borwein and Chen was used to show that for each k∈N the zeros of the hypergeometric polynomials F(-n, kn+1; kn+2; z) cluster on the loop of the lemniscate {z:zk(1-z)=kk/(k+1)k+1}, with Re{z}>k/(k+1) as n→∞. We now supply a direct proof which generalizes this result to arbitrary k>0, while showing that every point of the curve is a cluster point of zeros. Examples generated by computer graphics suggest some finer asymptotic properties of the zeros.

Original languageEnglish
Pages (from-to)329-343
Number of pages15
JournalJournal of Approximation Theory
Issue number2
StatePublished - Aug 2001

Bibliographical note

Funding Information:
1Both authors acknowledge support from the National Science Foundation. The paper is an outgrowth of a Research Experience for Undergraduates project at the University of Michigan.


  • Asymptotics
  • Hypergeometric polynomials
  • Zeros
  • lemniscates

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • General Mathematics
  • Applied Mathematics


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