Pólya frequency sequences and real zeros of some 3F2 polynomials

K. Driver; K. Jordaan; A. Martínez-Finkelshtein

doi:10.1016/j.jmaa.2006.10.080

Pólya frequency sequences and real zeros of some ₃F₂ polynomials

K. Driver, K. Jordaan, A. Martínez-Finkelshtein

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

We prove that the zeros of some families of ₃F₂ hypergeometric polynomials are all real and negative. This result has a connection with the theory of Pólya frequency sequences and functions. As a consequence, we establish the asymptotic distribution of these zeros when the degree of the polynomials tends to infinity.

Original language	English
Pages (from-to)	1045-1055
Number of pages	11
Journal	Journal of Mathematical Analysis and Applications
Volume	332
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2006.10.080
State	Published - 15 Aug 2007
Externally published	Yes

Keywords

F polynomials
Hypergeometric polynomials
Polynomials
Pólya frequency function
Pólya frequency sequences
Total positivity

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1016/j.jmaa.2006.10.080

Cite this

@article{fae731d0ead240de8a1cc6d68f2a3986,

title = "P{\'o}lya frequency sequences and real zeros of some 3F2 polynomials",

abstract = "We prove that the zeros of some families of 3F2 hypergeometric polynomials are all real and negative. This result has a connection with the theory of P{\'o}lya frequency sequences and functions. As a consequence, we establish the asymptotic distribution of these zeros when the degree of the polynomials tends to infinity.",

keywords = "F polynomials, Hypergeometric polynomials, Polynomials, P{\'o}lya frequency function, P{\'o}lya frequency sequences, Total positivity",

author = "K. Driver and K. Jordaan and A. Mart{\'i}nez-Finkelshtein",

year = "2007",

month = aug,

day = "15",

doi = "10.1016/j.jmaa.2006.10.080",

language = "English",

volume = "332",

pages = "1045--1055",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - Pólya frequency sequences and real zeros of some 3F2 polynomials

AU - Driver, K.

AU - Jordaan, K.

AU - Martínez-Finkelshtein, A.

PY - 2007/8/15

Y1 - 2007/8/15

N2 - We prove that the zeros of some families of 3F2 hypergeometric polynomials are all real and negative. This result has a connection with the theory of Pólya frequency sequences and functions. As a consequence, we establish the asymptotic distribution of these zeros when the degree of the polynomials tends to infinity.

AB - We prove that the zeros of some families of 3F2 hypergeometric polynomials are all real and negative. This result has a connection with the theory of Pólya frequency sequences and functions. As a consequence, we establish the asymptotic distribution of these zeros when the degree of the polynomials tends to infinity.

KW - F polynomials

KW - Hypergeometric polynomials

KW - Polynomials

KW - Pólya frequency function

KW - Pólya frequency sequences

KW - Total positivity

UR - https://www.scopus.com/pages/publications/34247363700

U2 - 10.1016/j.jmaa.2006.10.080

DO - 10.1016/j.jmaa.2006.10.080

M3 - Article

AN - SCOPUS:34247363700

SN - 0022-247X

VL - 332

SP - 1045

EP - 1055

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -