English

Zeros of Ramanujan Type Entire Functions

Classical Analysis and ODEs 2016-03-17 v2

Abstract

In this work we establish some polynomials and entire functions have only real zeros. These polynomials generalize q-Laguerre polynomials Ln(α)(x;q)L_{n}^{(\alpha)}(x;q), while the entire functions are generalizations of Ramanujan's entire function Aq(z)A_{q}(z), q-Bessel functions Jν(2)(z;q)J_{\nu}^{(2)}(z;q), Jν(3)(z;q)J_{\nu}^{(3)}(z;q) and confluent basic hypergeometric series.

Keywords

Cite

@article{arxiv.1603.04694,
  title  = {Zeros of Ramanujan Type Entire Functions},
  author = {Ruiming Zhang},
  journal= {arXiv preprint arXiv:1603.04694},
  year   = {2016}
}

Comments

10 pages

R2 v1 2026-06-22T13:11:23.290Z