Zeros of Ramanujan Type Entire Functions (1603.04694v2)

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.