``Best possible'' upper and lower bounds for

the zeros of the Bessel function

Authors:
C. K. Qu and R. Wong

Journal:
Trans. Amer. Math. Soc. **351** (1999), 2833-2859

MSC (1991):
Primary 41A60, 33C45

DOI:
https://doi.org/10.1090/S0002-9947-99-02165-0

Published electronically:
March 18, 1999

MathSciNet review:
1466955

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let denote the -th positive zero of the Bessel function . In this paper, we prove that for and , 2, 3, ,

These bounds coincide with the first few terms of the well-known asymptotic expansion

as , being fixed, where is the -th negative zero of the Airy function , and so are ``best possible''.

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Additional Information

**C. K. Qu**

Affiliation:
Department of Applied Mathematics, Tsinghua University, Beijing, China

**R. Wong**

Affiliation:
Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong

Email:
mawong@cityu.edu.hk

DOI:
https://doi.org/10.1090/S0002-9947-99-02165-0

Keywords:
Bessel functions,
zeros,
inequalities,
asymptotic expansions

Received by editor(s):
July 22, 1996

Received by editor(s) in revised form:
March 18, 1997

Published electronically:
March 18, 1999

Article copyright:
© Copyright 1999
American Mathematical Society