Zeros of Ramanujan Type Entire Functions

Ruiming Zhang

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arXiv · 1603.04694

Zeros of Ramanujan Type Entire Functions

Ruiming Zhang

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Abstract

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

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Ruiming Zhang. 2016-03-12. Zeros of Ramanujan Type Entire Functions. https://arxiv.org/abs/1603.04694

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