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)
On multiple zeros of derivatives of Bessel’s cylindrical functions. (English) Zbl 0611.33010
The authors discuss double zeros of the functions J ν (s) (z), Y ν (s) (z), s=1,2,3, where ν is real and z is complex. In the case s=0, there are no double zeros except possibly at the singular points 0, of the Bessel differential equation. For s=1, such ”nonsingular” zeros must lie on the curves z=±ν. The authors find similar curves in the cases s=2,3 and hence find asymptotic formulas for these possible zeros as ν±. They summarize the results of other investigations and computations. More details are to be found in the authors’ paper in Zh. Vychisl. Mat. Mat. Fiz. 25, No.12, 1749-1760 (1985; Zbl 0588.65015). A typical result is that there is a single ν n on each interval (-n-1,-n), n=1,2,···, for which J ν n ' (±z) has a double zero and -ν n =n+1/6+o(1), n. The interest in such double zeros arose in work of J. Lense in the 1930’s on conformal mappings implemented by Bessel functions and in recent work by the authors on the investigation and computation of complex zeros of cylinder functions.
Reviewer: M.E.Muldoon
MSC:
33C10Bessel and Airy functions, cylinder functions, 0 F 1
65D20Computation of special functions, construction of tables
30C15Zeros of polynomials, etc. (one complex variable)