On the conditions for a special entire function relative to the partial theta-function and the Euler function to belong to the Laguerre-P\'olya class

Thu Hien Nguyen

On the conditions for a special entire function relative to the partial theta-function and the Euler function to belong to the Laguerre-P\'olya class

Complex Variables 2019-12-24 v1 Functional Analysis

Authors: Thu Hien Nguyen

Abstract

In this paper, we discuss the conditions for the function $F_a(z) = \sum_{k=0}^\infty \frac{z^k}{(a+1)(a^2+1) \ldots (a^k+1)}, a>1,$ to belong to the Laguerre-P\'olya class, or to have only real zeros.

Keywords

entire function laguerre-pólya class partial theta-function euler function real zeros

Cite

@article{arxiv.1912.10035,
  title  = {On the conditions for a special entire function relative to the partial theta-function and the Euler function to belong to the Laguerre-P\'olya class},
  author = {Thu Hien Nguyen},
  journal= {arXiv preprint arXiv:1912.10035},
  year   = {2019}
}

Comments

19 pages, submitted to CMFT Journal. This article was partially supported by the Akhiezer Foundation. The author is also deeply grateful to her scientific advisor, A. Vishnyakova, for her patience, support and contribution to her research career. arXiv admin note: text overlap with arXiv:1903.09070

On the conditions for a special entire function relative to the partial theta-function and the Euler function to belong to the Laguerre-P\'olya class

Abstract

Keywords

Cite

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