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Uniform Asymptotic Expansion for the Incomplete Beta Function
Репозиторій DSpace/Manakin
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- Фізико-технічні та математичні науки
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12
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Uniform Asymptotic Expansion for the Incomplete Beta Function
Інший ID:
2010 Mathematics Subject Classification: 41A60; 33B20
DOI:10.3842/SIGMA.2016.101
DOI:10.3842/SIGMA.2016.101
Посилання:
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.
Підтримка:
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.
Дата:
2016
Переглядів:
557
Завантажень:
327
Анотація:
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.
