On an integral representation of a class of Kapteyn (Fourier–Bessel) series: Kepler’s equation, radiation problems and Meissel’s expansion

In this paper, an integral representation of a class of Kapteyn series is proposed. Such a representation includes the most used series in practical applications. The approach uses the property of uniform convergence of the considered class and the integral representation of the Bessel functions. Th...

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Bibliographic Details
Published inApplied mathematics letters Vol. 23; no. 11; pp. 1331 - 1335
Main Authors Eisinberg, A., Fedele, G., Ferrise, A., Frascino, D.
Format Journal Article
LanguageEnglish
Published Kidlington Elsevier Ltd 01.11.2010
Elsevier
Subjects
Bessel functions
Convergence
Exact sciences and technology
Fourier analysis
Fourier-Bessel transformations
Integrals
Kapteyn series
Kepler’s problem
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equations
Representations
Sciences and techniques of general use
Special functions
Kepler’s problem
Bessel functions
Kapteyn series
Uniform convergence
Bessel function
Kepler's problem
Applied mathematics
Integral equation
Function representation
Fourier series
Integral representation
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Summary:In this paper, an integral representation of a class of Kapteyn series is proposed. Such a representation includes the most used series in practical applications. The approach uses the property of uniform convergence of the considered class and the integral representation of the Bessel functions. The usefulness of the proposed method is highlighted by providing an integral solution of Kepler’s equation and of some Kapteyn series arising in radiation problems. Moreover it allows us to generalize a result due to Meissel.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0893-9659
1873-5452
DOI:10.1016/j.aml.2010.06.026