English

Partial fraction expansions and zeros of Hankel transforms

Classical Analysis and ODEs 2024-11-11 v2

Abstract

It is proved by the method of partial fraction expansions and Sturm's oscillation theory that the zeros of certain Hankel transforms are all real and distributed regularly between consecutive zeros of Bessel functions. As an application, the sufficient or necessary conditions on parameters for which 1F2{}_1F_2 hypergeometric functions belong to the Laguerre-P\'olya class are investigated in a constructive manner.

Keywords

Cite

@article{arxiv.2311.04385,
  title  = {Partial fraction expansions and zeros of Hankel transforms},
  author = {Yong-Kum Cho and Seok-Young Chung and Young Woong Park},
  journal= {arXiv preprint arXiv:2311.04385},
  year   = {2024}
}