Geodesic
Uniform Asymptotic Expansion for the Incomplete Beta Function
Symmetry, integrability and geometry: methods and applications, Tome 12 (2016) Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{SIGMA_2016_12_a100,
     author = {Gerg\H{o} Nemes and Adri B. Olde Daalhuis},
     title = {Uniform {Asymptotic} {Expansion} for the {Incomplete} {Beta} {Function}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2016},
     volume = {12},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a100/}
}
TY  - JOUR
AU  - Gergő Nemes
AU  - Adri B. Olde Daalhuis
TI  - Uniform Asymptotic Expansion for the Incomplete Beta Function
JO  - Symmetry, integrability and geometry: methods and applications
PY  - 2016
VL  - 12
UR  - http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a100/
LA  - en
ID  - SIGMA_2016_12_a100
ER  - 
%0 Journal Article
%A Gergő Nemes
%A Adri B. Olde Daalhuis
%T Uniform Asymptotic Expansion for the Incomplete Beta Function
%J Symmetry, integrability and geometry: methods and applications
%D 2016
%V 12
%U http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a100/
%G en
%F SIGMA_2016_12_a100
Gergő Nemes; Adri B. Olde Daalhuis. Uniform Asymptotic Expansion for the Incomplete Beta Function. Symmetry, integrability and geometry: methods and applications, Tome 12 (2016). http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a100/

[1] Johnson N. L., Kotz S., Balakrishnan N., Continuous univariate distributions, v. 2, Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics, 2nd ed., John Wiley Sons, Inc., New York, 1995 | MR

[2] Olver F. W. J., Lozier D. W., Boisvert R. F., Clark C. W. (eds.), NIST handbook of mathematical functions, Release 1.0.13 of 2016-09-16, , U.S. Department of Commerce, National Institute of Standards and Technology, Washington, DC; Cambridge University Press, Cambridge, 2010 http://dlmf.nist.gov/ | MR

[3] 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 | DOI | MR

[4] Temme N. M., Asymptotic methods for integrals, Series in Analysis, 6, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2015 | DOI | MR | Zbl