Uniform representations of the incomplete beta function in terms of elementary functions

zbMath1406.33002MaRDI QIDQ1716838

Chelo Ferreira, Ester Pérez Sinusía, José Luis López

Publication date: 5 February 2019

Published in: ETNA. Electronic Transactions on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: http://etna.mcs.kent.edu/volumes/2011-2020/vol48/abstract.php?vol=48&pages=450-461

zbMATH Keywords

incomplete beta functionuniform expansionsconvergent expansions

Mathematics Subject Classification ID

Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58) Remainders in approximation formulas (41A80) Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) (33B20)

Related Items (6)

On the antiderivatives of \(x^p/(1 - x)\) with an application to optimize loss functions for classification with neural networks ⋮ An analytic representation of the second symmetric standard elliptic integral in terms of elementary functions ⋮ Uniform convergent expansions of the error function in terms of elementary functions ⋮ Uniform approximations of the first symmetric elliptic integral in terms of elementary functions ⋮ Incomplete beta polynomials ⋮ The series expansions and Gauss-Legendre rule for computing arbitrary derivatives of the beta-type functions

Uses Software

• DLMF

Cites Work

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• Uniform asymptotic expansion for the incomplete beta function
• A simplification of Laplace's method: applications to the gamma function and Gauss hypergeometric function
• Convergent expansions of the Bessel functions in terms of elementary functions
• Uniform Asymptotic Expansions of the Incomplete Gamma Functions and the Incomplete Beta Function
• Convergent expansions of the incomplete gamma functions in terms of elementary functions

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