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 numerical evaluation of integrals involving Bessel functions. (English) Zbl 0614.65012

The authors discuss the numerical computation of the integral

I= 0 f(x)J n (rx)dx

for fixed integer n0 and a given set of real values of r. In a first approach, they replace the Bessel function J n (x) by a well-known trigonometric integral and then compute I by using a fast Fourier transform procedure. The second method consists of the construction of weights and abscissas for a Gaussian integration formula with J n (x) a weight function over the intervals between two consecutive zeros of J n (x). A comparison shows that the second method, once the weights and abscissas have been obtained, is more efficient. A table of weights and abscissas for a five- point Gauss rule is given and an error analysis is presented. An appropriate application of any of the existing adaptive quadrature procedures is not discussed.

Reviewer: K.S.Kölbig

MSC:
65D20Computation of special functions, construction of tables
65T40Trigonometric approximation and interpolation (numerical methods)
65D32Quadrature and cubature formulas (numerical methods)
33C10Bessel and Airy functions, cylinder functions, 0 F 1
42A16Fourier coefficients, special Fourier series, etc.