zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Computing zeros and orders of Bessel functions. (English) Zbl 0758.65011
This paper contains the development of an algorithm and convergence analysis that is needed for the construction of software for finding zeros of Bessel functions $J\sb m(x)$. The authors consider computing a prescribed number of smallest positive zeros of Bessel functions and of their derivatives of a prescribed order within a prescribed relative error. They also discuss the inverse problems for finding the order of the Bessel function that has a zero of a prescribed order at a prescribed positive value.

MSC:
65D20Computation of special functions, construction of tables
65H05Single nonlinear equations (numerical methods)
33C10Bessel and Airy functions, cylinder functions, ${}_0F_1$
Software:
EISPACK
WorldCat.org
Full Text: DOI
References:
[1] Abramowitz, M.; Stegun, I. A.: Handbook of mathematical functions. (1972) · Zbl 0543.33001
[2] Akhiezer, N. I.; Glazman, I. M.: Theory of linear operators in Hilbert space, volume 1. (1981) · Zbl 0467.47001
[3] Bowman, F.: Introduction to Bessel functions. (1958) · Zbl 0083.05602
[4] Elbert, A.; Laforgia, A.: Further results on the zeros of Bessel functions. Analysis 5, 71-86 (1985) · Zbl 0564.33005
[5] Grad, J.; Zakrajs\tilde{}ek, E.: Method for evaluation of zeros of Bessel functions. J. inst. Math. appl. 11, 57-72 (1973) · Zbl 0252.33007
[6] Hochstadt, H.: The functions of mathematical physics. (1971) · Zbl 0217.39501
[7] Ikebe, Y.: The zeros of regular Coulomb wave functions and of their derivatives. Math. comp. 29, 878-887 (1975) · Zbl 0308.65015
[8] Li, T. Y.; Rhee, N. H.: Homotopy algorithm for symmetric eigenvalue problems. Numer. math. 55, 265-280 (1989) · Zbl 0653.65025
[9] Lorch, L.: Monotonicity in terms of order of the zeros of the derivatives of Bessel functions. Proc. amer. Math. soc. 108, 387-389 (1990) · Zbl 0693.33004
[10] Lorch, L.; Szego?, P.: On the zeros of derivatives of Bessel functions. SIAM J. Math. anal. 19, 1450-1454 (1988) · Zbl 0666.33006
[11] Magnus, W.; Oberhettinger, F.; Soni, R. P.: Formulas and theorems for the special functions of mathematical physics. (1966) · Zbl 0143.08502
[12] Smith, B. T.; Boyle, J. M.; Dongarra, J. J.; Garbow, B. S.; Ikebe, Y.; Klema, V. C.; Moler, C. B.: Matrix eigensystem routines -- EISPACK guide. (1976)
[13] Watson, G. N.: A treatise on the theory of Bessel functions. (1966) · Zbl 0174.36202
[14] Wilkinson, J. H.: The algebraic eigenvalue problem. (1965) · Zbl 0258.65037
[15] . (1989)