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arxiv: 1603.04694 · v2 · pith:XNKZ666Znew · submitted 2016-03-12 · 🧮 math.CA

Zeros of Ramanujan Type Entire Functions

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keywords entirefunctionspolynomialsramanujanzerosalphabasicconfluent
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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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