Zeros of Ramanujan Type Entire Functions

2016/03/12 by Zhang, Ruiming
#33C10 #33C99 #33D15 #33D99 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1603.04694

Abstract

In this work we establish some polynomials and entire functions have only real zeros. These polynomials generalize q-Laguerre polynomials L_n^(α)(x;q), while the entire functions are generalizations of Ramanujan's entire function A_q(z), q-Bessel functions J_ν⁽²⁾(z;q), J_ν⁽³⁾(z;q) and confluent basic hypergeometric series.

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