Criterion of the reality of zeros in a polynomial sequence satisfying a three-term recurrence relation
Czechoslovak Mathematical Journal (2020)
- Volume: 70, Issue: 3, page 793-804
- ISSN: 0011-4642
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topNdikubwayo, Innocent. "Criterion of the reality of zeros in a polynomial sequence satisfying a three-term recurrence relation." Czechoslovak Mathematical Journal 70.3 (2020): 793-804. <http://eudml.org/doc/297200>.
@article{Ndikubwayo2020,
abstract = {This paper establishes the necessary and sufficient conditions for the reality of all the zeros in a polynomial sequence $\lbrace P_i\rbrace _\{i=1\}^\{\infty \}$ generated by a three-term recurrence relation $P_i(x)+ Q_1(x)P_\{i-1\}(x) +Q_2(x) P_\{i-2\}(x)=0$ with the standard initial conditions $P_\{0\}(x)=1, P_\{-1\}(x)=0,$ where $Q_1(x)$ and $Q_2(x)$ are arbitrary real polynomials.},
author = {Ndikubwayo, Innocent},
journal = {Czechoslovak Mathematical Journal},
keywords = {recurrence relation; polynomial sequence; support; real zeros},
language = {eng},
number = {3},
pages = {793-804},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Criterion of the reality of zeros in a polynomial sequence satisfying a three-term recurrence relation},
url = {http://eudml.org/doc/297200},
volume = {70},
year = {2020},
}
TY - JOUR
AU - Ndikubwayo, Innocent
TI - Criterion of the reality of zeros in a polynomial sequence satisfying a three-term recurrence relation
JO - Czechoslovak Mathematical Journal
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 70
IS - 3
SP - 793
EP - 804
AB - This paper establishes the necessary and sufficient conditions for the reality of all the zeros in a polynomial sequence $\lbrace P_i\rbrace _{i=1}^{\infty }$ generated by a three-term recurrence relation $P_i(x)+ Q_1(x)P_{i-1}(x) +Q_2(x) P_{i-2}(x)=0$ with the standard initial conditions $P_{0}(x)=1, P_{-1}(x)=0,$ where $Q_1(x)$ and $Q_2(x)$ are arbitrary real polynomials.
LA - eng
KW - recurrence relation; polynomial sequence; support; real zeros
UR - http://eudml.org/doc/297200
ER -
References
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