The Asymptotic Expansion of Kummer Functions for Large Values of the α-Parameter, and Remarks on a Paper by Olver
It is shown that a known asymptotic expansion of the Kummer function U(a,b,z) as a tends to infinity is valid for z on the full Riemann surface of the logarithm. A corresponding result is also proved in a more general setting considered by Olver (1956).
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2016 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2016
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147735 |
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| Zitieren: | The Asymptotic Expansion of Kummer Functions for Large Values of the α-Parameter, and Remarks on a Paper by Olver / H. Volkmer // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 9 назв. — англ. |
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nasplib_isofts_kiev_ua-123456789-147735 |
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Volkmer, H. 2019-02-15T18:54:54Z 2019-02-15T18:54:54Z 2016 The Asymptotic Expansion of Kummer Functions for Large Values of the α-Parameter, and Remarks on a Paper by Olver / H. Volkmer // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 9 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 33B20; 33C15; 41A60 DOI:10.3842/SIGMA.2016.046 https://nasplib.isofts.kiev.ua/handle/123456789/147735 It is shown that a known asymptotic expansion of the Kummer function U(a,b,z) as a tends to infinity is valid for z on the full Riemann surface of the logarithm. A corresponding result is also proved in a more general setting considered by Olver (1956). This paper is a contribution to the Special Issue on Orthogonal Polynomials, Special Functions and Applications. The full collection is available at http://www.emis.de/journals/SIGMA/OPSFA2015.html. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Asymptotic Expansion of Kummer Functions for Large Values of the α-Parameter, and Remarks on a Paper by Olver Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
The Asymptotic Expansion of Kummer Functions for Large Values of the α-Parameter, and Remarks on a Paper by Olver |
| spellingShingle |
The Asymptotic Expansion of Kummer Functions for Large Values of the α-Parameter, and Remarks on a Paper by Olver Volkmer, H. |
| title_short |
The Asymptotic Expansion of Kummer Functions for Large Values of the α-Parameter, and Remarks on a Paper by Olver |
| title_full |
The Asymptotic Expansion of Kummer Functions for Large Values of the α-Parameter, and Remarks on a Paper by Olver |
| title_fullStr |
The Asymptotic Expansion of Kummer Functions for Large Values of the α-Parameter, and Remarks on a Paper by Olver |
| title_full_unstemmed |
The Asymptotic Expansion of Kummer Functions for Large Values of the α-Parameter, and Remarks on a Paper by Olver |
| title_sort |
asymptotic expansion of kummer functions for large values of the α-parameter, and remarks on a paper by olver |
| author |
Volkmer, H. |
| author_facet |
Volkmer, H. |
| publishDate |
2016 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
It is shown that a known asymptotic expansion of the Kummer function U(a,b,z) as a tends to infinity is valid for z on the full Riemann surface of the logarithm. A corresponding result is also proved in a more general setting considered by Olver (1956).
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/147735 |
| citation_txt |
The Asymptotic Expansion of Kummer Functions for Large Values of the α-Parameter, and Remarks on a Paper by Olver / H. Volkmer // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 9 назв. — англ. |
| work_keys_str_mv |
AT volkmerh theasymptoticexpansionofkummerfunctionsforlargevaluesoftheαparameterandremarksonapaperbyolver AT volkmerh asymptoticexpansionofkummerfunctionsforlargevaluesoftheαparameterandremarksonapaperbyolver |
| first_indexed |
2025-12-07T21:18:54Z |
| last_indexed |
2025-12-07T21:18:54Z |
| _version_ |
1850885888754581504 |