Zeros of Ramanujan type entire functions

Zhang, Ruiming

doi:10.1090/proc/13205

Zeros of Ramanujan type entire functions
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by Ruiming Zhang PDF

Proc. Amer. Math. Soc. 145 (2017), 241-250 Request permission

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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