Uniform Asymptotic Expansion for the Incomplete Beta Function
In [Temme N.M., Special functions. An introduction to the classical functions of mathematical physics, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1996, Section 11.3.3.1] a uniform asymptotic expansion for the incomplete beta function was derived. It was not obvious...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2016 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2016
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148002 |
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| Cite this: | Uniform Asymptotic Expansion for the Incomplete Beta Function / G. Nemes, A.B. Olde Daalhuis // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 4 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862551733360656384 |
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| author | Nemes, G. Olde Daalhuis, A.B. |
| author_facet | Nemes, G. Olde Daalhuis, A.B. |
| citation_txt | Uniform Asymptotic Expansion for the Incomplete Beta Function / G. Nemes, A.B. Olde Daalhuis // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 4 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In [Temme N.M., Special functions. An introduction to the classical functions of mathematical physics, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1996, Section 11.3.3.1] a uniform asymptotic expansion for the incomplete beta function was derived. It was not obvious from those results that the expansion is actually an asymptotic expansion. We derive a remainder estimate that clearly shows that the result indeed has an asymptotic property, and we also give a recurrence relation for the coefficients.
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| first_indexed | 2025-11-25T20:55:48Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148002 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-25T20:55:48Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Nemes, G. Olde Daalhuis, A.B. 2019-02-16T16:26:10Z 2019-02-16T16:26:10Z 2016 Uniform Asymptotic Expansion for the Incomplete Beta Function / G. Nemes, A.B. Olde Daalhuis // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 4 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 41A60; 33B20 DOI:10.3842/SIGMA.2016.101 https://nasplib.isofts.kiev.ua/handle/123456789/148002 In [Temme N.M., Special functions. An introduction to the classical functions of mathematical physics, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1996, Section 11.3.3.1] a uniform asymptotic expansion for the incomplete beta function was derived. It was not obvious from those results that the expansion is actually an asymptotic expansion. We derive a remainder estimate that clearly shows that the result indeed has an asymptotic property, and we also give a recurrence relation for the coefficients. This research was supported by a research grant (GRANT11863412/70NANB15H221) from the
 National Institute of Standards and Technology. The authors thank the anonymous referees for
 their helpful comments and suggestions on the manuscript. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Uniform Asymptotic Expansion for the Incomplete Beta Function Article published earlier |
| spellingShingle | Uniform Asymptotic Expansion for the Incomplete Beta Function Nemes, G. Olde Daalhuis, A.B. |
| title | Uniform Asymptotic Expansion for the Incomplete Beta Function |
| title_full | Uniform Asymptotic Expansion for the Incomplete Beta Function |
| title_fullStr | Uniform Asymptotic Expansion for the Incomplete Beta Function |
| title_full_unstemmed | Uniform Asymptotic Expansion for the Incomplete Beta Function |
| title_short | Uniform Asymptotic Expansion for the Incomplete Beta Function |
| title_sort | uniform asymptotic expansion for the incomplete beta function |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148002 |
| work_keys_str_mv | AT nemesg uniformasymptoticexpansionfortheincompletebetafunction AT oldedaalhuisab uniformasymptoticexpansionfortheincompletebetafunction |