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JOURNALS // Symmetry, Integrability and Geometry: Methods and Applications // Archive

SIGMA, 2016 Volume 12, 101, 5 pp. (Mi sigma1183)

This article is cited in 5 papers

Uniform Asymptotic Expansion for the Incomplete Beta Function

Gergő Nemes, Adri B. Olde Daalhuis

Maxwell Institute and School of Mathematics, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK

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.

Keywords: incomplete beta function; uniform asymptotic expansion.

MSC: 41A60; 33B20

Received: September 12, 2016; in final form October 21, 2016; Published online October 25, 2016

Language: English

DOI: 10.3842/SIGMA.2016.101



Bibliographic databases:
ArXiv: 1609.02827


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