No Access

ASYMPTOTICS OF ZEROS OF CERTAIN ENTIRE FUNCTIONS

MOURAD E. H. ISMAIL

Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA

https://doi.org/10.1142/S0219530507000997Cited by:0 (Source: Crossref)

Abstract

We derive representations for some entire q-functions and use it to derive asymptotics and closed form expressions for large zeros of a class of entire functions including the Ramanujan function, and q-Bessel functions.

Keywords:

AMSC: 30D10, 33D45

References

G. E. Andrews, Adv. Math. 191, 393 (2005), DOI: 10.1016/j.aim.2004.03.013. Crossref, Web of Science, Google Scholar
G. E. Andrews, Adv. Math. 191, 408 (2005), DOI: 10.1016/j.aim.2004.03.013. Crossref, Web of Science, Google Scholar
G. E. Andrews , R. A. Askey and R. Roy , Special Functions ( Cambridge University Press , Cambridge , 1999 ) . Crossref, Google Scholar
P. Deift , Orthogonal Polynomials and Random Matrices: A Riemann–Hilbert Approach ( New York University Courant Institute of Mathematical Sciences , New York , 1999 ) . Google Scholar
G. Gasper and M. Rahman , Basic Hypergeometric Series , 2nd edn. ( Cambridge University Press , Cambridge , 2004 ) . Crossref, Google Scholar
W. K. Hayman, Complex Analysis and Dynamical Systems II, Contemporary Mathematics 382 (American Mathematical Society, Providence, 2005) pp. 205–216. Crossref, Google Scholar
M. E. H. Ismail, J. Math. Anal. Appl. 86, 1 (1982), DOI: 10.1016/0022-247X(82)90248-7. Crossref, Web of Science, Google Scholar
M. E. H. Ismail, Int. Math. Res. Not. 18, 1063 (2005). Google Scholar
M. E. H. Ismail , Classical and Quantum Orthogonal Polynomials in One Variable ( Cambridge University Press , Cambridge , 2005 ) . Crossref, Google Scholar
M. E. H. Ismail and C. Zhang, Zeros of entire functions and a problem of Ramanujan, Adv. Math. to appear . Google Scholar
K. Kajiwaraet al., Int. Math. Res. Not. 47, 2497 (2004). Google Scholar
M. L. Mehta , Random Matrices , 3rd edn. ( Elsevier , Amsterdam , 2004 ) . Google Scholar
W.-Y. Qiu and R. Wong, SIAM J. Math. Anal. 31, 992 (2000), DOI: 10.1137/S0036141098344671. Crossref, Web of Science, Google Scholar
S. Ramanujan , The Lost Notebook and Other Unpublished Papers ( Narosa , New Delhi , 1988 ) . Google Scholar
G. Szegő, Orthogonal Polynomials, 4th edn. (Amer. Math. Soc., Providence, 1975). Google Scholar
E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, 4th edn. (Cambridge University Press, Cambridge, 1927). Google Scholar