Criterion of the reality of zeros in a polynomial sequence satisfying a three-term recurrence relation.

Autor: Ndikubwayo, Innocent
Jazyk: angličtina
Předmět:
Druh dokumentu: Non-fiction
ISSN: 0011-4642
Abstrakt: Abstract: This paper establishes the necessary and sufficient conditions for the reality of all the zeros in a polynomial sequence $\{P_i\}_{i=1}^{\infty}$ 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.
Databáze: Katalog Knihovny AV ČR
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