Uniform Asymptotic Expansion for the Incomplete Beta Function

Gergo Nemes; Adri Olde Daalhuis

doi:10.3842/SIGMA.2016.101

Uniform Asymptotic Expansion for the Incomplete Beta Function

Gergo Nemes, Adri Olde Daalhuis

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Article number	101
Number of pages	5
Journal	Symmetry, Integrability and Geometry : Methods and Applications
Volume	12
DOIs	https://doi.org/10.3842/SIGMA.2016.101
Publication status	Published - 25 Oct 2016

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10.3842/SIGMA.2016.101

1609.02827v2Accepted author manuscript, 269 KB

Rigorous and Presentable Asymptotics for Special Functions and Orthogonal Polynomials
Olde Daalhuis, A.
Non-EU other
1/09/15 → 31/08/20
Project: Research

Cite this

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AB - 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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DO - 10.3842/SIGMA.2016.101

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Uniform Asymptotic Expansion for the Incomplete Beta Function

Abstract

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Rigorous and Presentable Asymptotics for Special Functions and Orthogonal Polynomials

Cite this