Zeros of Ramanujan Type Entire Functions

preprint2016arXivOpen access

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}^{(α)}(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_ν^{(2)}(z;q), Jν(3)(z;q)J_ν^{(3)}(z;q) and confluent basic hypergeometric series.

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