Uniform Asymptotic Expansion for the Incomplete Beta Function
Classical Analysis and ODEs
2016-10-26 v2
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.
Cite
@article{arxiv.1609.02827,
title = {Uniform Asymptotic Expansion for the Incomplete Beta Function},
author = {Gergő Nemes and Adri B. Olde Daalhuis},
journal= {arXiv preprint arXiv:1609.02827},
year = {2016}
}