Zeros of Ramanujan type entire functions
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- by Ruiming Zhang PDF
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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.References
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Additional Information
- Ruiming Zhang
- Affiliation: College of Science, Northwest A&F University, Yangling, Shaanxi 712100, People’s Republic of China
- MR Author ID: 257230
- Received by editor(s): March 12, 2016
- Received by editor(s) in revised form: March 16, 2016
- Published electronically: July 7, 2016
- Additional Notes: This research was partially supported by National Natural Science Foundation of China, grant No. 11371294 and Northwest A&F University of China.
- Communicated by: Mourad Ismail
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 241-250
- MSC (2010): Primary 33D15, 33C10, 33D99, 33C99
- DOI: https://doi.org/10.1090/proc/13205
- MathSciNet review: 3565376