An asymptotic expansion for the incomplete beta function

DOI10.1090/S0025-5718-96-00729-6zbMath0854.33003MaRDI QIDQ4889934

Brian George Spencer Doman

Publication date: 11 August 1996

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

incomplete beta function

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Computation of special functions and constants, construction of tables (65D20) Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) (33B20)

Related Items (5)

The series expansions and Gauss-Legendre rule for computing arbitrary derivatives of the beta-type functions ⋮ An extension of the incomplete beta function for negative integers ⋮ On partial derivatives of the incomplete beta function ⋮ Asymptotic expansions of intgrals: The term-by-term integration method ⋮ Asymptotic expansion Of the incomplete beta function for large values Of the first parameter

Uses Software

• BRATIO

Cites Work

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• The special functions and their approximations. Vol. I, II
• Error Bounds for Asymptotic Expansions of the Ratio of Two Gamma Functions
• Computation of the incomplete gamma function ratios and their inverse
• Incomplete Laplace Integrals: Uniform Asymptotic Expansion with Application to the Incomplete Beta Function
• An Expansion for Laplacian Integrals in Terms of Incomplete Gamma Functions, and Some Applications*
• A set of Ada packages for high-precision calculations
• Algorithm 708: Significant digit computation of the incomplete beta function ratios
• A Note on the Asymptotic Expansion of a Ratio of Gamma Functions
• THE INCOMPLETE BETA FUNCTION AS A CONTOUR INTEGRAL AND A QUICKLY CONVERGING SERIES FOR ITS INVERSE

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