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 from...
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| Видавець: | Інститут математики НАН України |
|---|---|
| Дата: | 2016 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2016
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/148002 |
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| Цитувати: | 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| id |
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irk-123456789-1480022019-02-17T01:25:18Z Uniform Asymptotic Expansion for the Incomplete Beta Function Nemes, G. Olde Daalhuis, A.B. 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. 2016 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/148002 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Nemes, G. Olde Daalhuis, A.B. |
| spellingShingle |
Nemes, G. Olde Daalhuis, A.B. Uniform Asymptotic Expansion for the Incomplete Beta Function Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Nemes, G. Olde Daalhuis, A.B. |
| author_sort |
Nemes, G. |
| title |
Uniform Asymptotic Expansion for the Incomplete Beta Function |
| title_short |
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_sort |
uniform asymptotic expansion for the incomplete beta function |
| publisher |
Інститут математики НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148002 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT nemesg uniformasymptoticexpansionfortheincompletebetafunction AT oldedaalhuisab uniformasymptoticexpansionfortheincompletebetafunction |
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2023-05-20T17:29:00Z |
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2023-05-20T17:29:00Z |
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1796153397083111424 |