Zeros of Meixner and Krawtchouk polynomials

Details Zeros of Meixner and Krawtchouk polynomials Zeros of Meixner and Krawtchouk polynomials

2009-01-07

arxiv.org/abs/0901.0817v3

Mathematics

Classical Analysis and ODEs

Scientific paper

We investigate the zeros of a family of hypergeometric polynomials $_2F_1(-n,-x;a;t)$, $n\in\nn$ that are known as the Meixner polynomials for certain values of the parameters $a$ and $t$. When $a=-N$, $N\in\nn$ and $t=\frac1{p}$, the polynomials $K_n(x;p,N)=(-N)_n\phantom{}_2F_1(-n,-x;-N;\frac1{p})$, $n=0,1,...N$, $0n-1$, the quasi-orthogonal polynomials $K_{n}(x;p,a)$, $k-11$ or $p<0$ as well as the non-orthogonal polynomials $K_{n}(x;p,N)$, $0

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