### Abstract

We establish some representations for the smallest and largest zeros of orthogonal polynomials in terms of the parameters in the three-terms recurrence relation. As a corollary we obtain representations for the endpoints of the true interval of orthogonality. Implications of these results for the decay parameter of a birth death process (with killing) are displayed.

Original language | Undefined |
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Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Number of pages | 9 |

Publication status | Published - Aug 2007 |

### Publication series

Name | Memorandum / Department of Applied Mathematics |
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Publisher | University of Twente, Department of Computer Science |

No. | LNCS4549/1850 |

ISSN (Print) | 1874-4850 |

ISSN (Electronic) | 1874-4850 |

### Keywords

- Birth-death process
- IR-64326
- MSC-60J80
- MSC-42C05
- EWI-10994
- Interval of orthogonality
- Decay parameter
- METIS-241876
- Three-terms recurrence relation

## Cite this

van Doorn, E. A., van Foreest, N. D., & Zeifman, A. I. (2007).

*Representations for the extreme zeros of orthogonal polynomials*. (Memorandum / Department of Applied Mathematics; No. LNCS4549/1850). Enschede: University of Twente, Department of Applied Mathematics.