Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

Request Permissions   Purchase Content 
 

 

Zeros of Ramanujan type entire functions


Author: Ruiming Zhang
Journal: Proc. Amer. Math. Soc. 145 (2017), 241-250
MSC (2010): Primary 33D15, 33C10, 33D99, 33C99
DOI: https://doi.org/10.1090/proc/13205
Published electronically: July 7, 2016
MathSciNet review: 3565376
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 33D15, 33C10, 33D99, 33C99

Retrieve articles in all journals with MSC (2010): 33D15, 33C10, 33D99, 33C99


Additional Information

Ruiming Zhang
Affiliation: College of Science, Northwest A&F University, Yangling, Shaanxi 712100, People’s Republic of China

DOI: https://doi.org/10.1090/proc/13205
Keywords: Zeros of polynomials, zeros of q-series, Laguerre-P\'olya class, P\'olya frequence sequence, q-Laguerre polynomials, q-Bessel functions, basic hypergeometric series.
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
Article copyright: © Copyright 2016 American Mathematical Society