A Review of Procedures for Summing Kapteyn Series in Mathematical Physics
Since the discussion of Kapteyn series occurrences in astronomical problems the wealth of mathematical physics problems in which such series play dominant roles has burgeoned massively. One of the major concerns is the ability to sum such series in closed form so that one can better understand the s...
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2009/425164 |
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| author | R. C. Tautz I. Lerche |
| author_facet | R. C. Tautz I. Lerche |
| author_sort | R. C. Tautz |
| collection | DOAJ |
| description | Since the discussion of Kapteyn series occurrences in astronomical problems the wealth of
mathematical physics problems in which such series play dominant roles has burgeoned massively. One of the major concerns is the ability to sum such series in closed form so that one can better understand the structural and functional behavior of the basic physics
problems. The purpose of this review article is to present some of the recent methods for providing such series in closed form with applications to: (i) the summation of Kapteyn series for radiation from pulsars; (ii) the summation of other Kapteyn series in radiation problems; (iii) Kapteyn series arising in terahertz sideband spectra of quantum systems modulated by an alternating electromagnetic field; and (iv) some plasma problems involving sums of Bessel functions and their closed form summation using variations of the techniques developed for Kapteyn series. In addition, a short review is given of some other Kapteyn series to illustrate the ongoing deep interest and involvement of scientists in such problems and to provide further techniques for attempting to sum divers Kapteyn series. |
| format | Article |
| id | doaj-art-edb48895e22a453fb10ff977239048c5 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-edb48895e22a453fb10ff977239048c52025-02-03T01:01:35ZengWileyAdvances in Mathematical Physics1687-91201687-91392009-01-01200910.1155/2009/425164425164A Review of Procedures for Summing Kapteyn Series in Mathematical PhysicsR. C. Tautz0I. Lerche1Astronomical Institute, Universiteit Utrecht, Princetonplein 5, NL-3584CC Utrecht, The NetherlandsInstitut für Geowissenschaften, Naturwissenschaftliche Fakultät III, Martin-Luther-Universität Halle, 06099 Halle, GermanySince the discussion of Kapteyn series occurrences in astronomical problems the wealth of mathematical physics problems in which such series play dominant roles has burgeoned massively. One of the major concerns is the ability to sum such series in closed form so that one can better understand the structural and functional behavior of the basic physics problems. The purpose of this review article is to present some of the recent methods for providing such series in closed form with applications to: (i) the summation of Kapteyn series for radiation from pulsars; (ii) the summation of other Kapteyn series in radiation problems; (iii) Kapteyn series arising in terahertz sideband spectra of quantum systems modulated by an alternating electromagnetic field; and (iv) some plasma problems involving sums of Bessel functions and their closed form summation using variations of the techniques developed for Kapteyn series. In addition, a short review is given of some other Kapteyn series to illustrate the ongoing deep interest and involvement of scientists in such problems and to provide further techniques for attempting to sum divers Kapteyn series.http://dx.doi.org/10.1155/2009/425164 |
| spellingShingle | R. C. Tautz I. Lerche A Review of Procedures for Summing Kapteyn Series in Mathematical Physics Advances in Mathematical Physics |
| title | A Review of Procedures for Summing Kapteyn Series in Mathematical Physics |
| title_full | A Review of Procedures for Summing Kapteyn Series in Mathematical Physics |
| title_fullStr | A Review of Procedures for Summing Kapteyn Series in Mathematical Physics |
| title_full_unstemmed | A Review of Procedures for Summing Kapteyn Series in Mathematical Physics |
| title_short | A Review of Procedures for Summing Kapteyn Series in Mathematical Physics |
| title_sort | review of procedures for summing kapteyn series in mathematical physics |
| url | http://dx.doi.org/10.1155/2009/425164 |
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