UNIFORM UPPER AND LOWER BOUNDS ON THE ZEROS OF BESSEL-FUNCTIONS OF THE FIRST KIND

被引:19
作者
BREEN, S
机构
[1] California State Universtiy Northridge, Department of mathmetics, Northridge
关键词
D O I
10.1006/jmaa.1995.1395
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We derive upper and lower bounds to the kth positive zero of the Bessel function of the first kind of order v. These bounds are close to the known asymptotic formulas which are valid only when k or v are very large. Applications are discussed and upper and lower bounds to the zeros of the Airy function are also derived. (C) 1995 Academic Press, Inc.
引用
收藏
页码:1 / 17
页数:17
相关论文
共 13 条
  • [1] Abramowitz M., 1970, HDB MATH FUNCTIONS
  • [2] [Anonymous], 1954, PHILOS T R SOC LON A, DOI DOI 10.1098/RSTA.1954.0021
  • [3] Coddington E.A., 1955, THEORY ORDINARY DIFF
  • [4] AN APPROXIMATION FOR THE ZEROS OF BESSEL-FUNCTIONS
    ELBERT, A
    [J]. NUMERISCHE MATHEMATIK, 1991, 59 (07) : 647 - 657
  • [5] AN ASYMPTOTIC RELATION FOR THE ZEROS OF BESSEL-FUNCTIONS
    ELBERT, A
    LAFORGIA, A
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1984, 98 (02) : 502 - 511
  • [6] Erdelyi A., 1965, ASYMPTOTIC EXPANSION
  • [7] HOCHSTADT H, 1986, FUNCTIONS MATH PHYSI
  • [8] Olver F. W. J., 1954, PHILOS T R SOC A, V247, P307, DOI DOI 10.1098/RSTA.1954.0020
  • [9] OLVER FWJ, 1974, ASYMPTOTICS SPECIAL
  • [10] Polya G, 1954, MATH PLAUSIBLE REASO, V2