The series expansions and Gauss-Legendre rule for computing arbitrary derivatives of the beta-type functions

DOI10.1553/ETNA_VOL52S203OpenAlexW3014292406MaRDI QIDQ1988492

Tongke Wang, Yonghong Hao, Jun-lin Li

Publication date: 23 April 2020

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/vol52/abstract.php?vol=52&pages=203-213

zbMATH Keywords

series expansionbeta-type functionshigher-order partial derivativesmodified Gauss-Legendre rule

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Computation of special functions and constants, construction of tables (65D20) Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) (33B20)

Related Items (2)

Singular asymptotic expansion and Legendre collocation method for two-term weakly singular Volterra integral equation of the second kind ⋮ Singular expansions and collocation methods for generalized Abel integral equations

Uses Software

• BRATIO
• DLMF

Cites Work

• Uniform asymptotic expansion for the incomplete beta function
• Extension of the partial derivatives of the incomplete beta function for complex values
• On partial derivatives of the incomplete beta function
• Asymptotic inversion of the incomplete beta function
• Uniform representations of the incomplete beta function in terms of elementary functions
• An algorithm for the inversion of Laplace transforms using Puiseux expansions
• An extension of the incomplete beta function for negative integers
• The modified composite Gauss type rules for singular integrals using Puiseux expansions
• Uniform Asymptotic Expansions of the Incomplete Gamma Functions and the Incomplete Beta Function
• Algorithm 708: Significant digit computation of the incomplete beta function ratios
• An asymptotic expansion for the incomplete beta function
• The Incomplete Beta Function and its Ratio to the Complete Beta Function
• On the computation of a certain type of incomplete Beta functions
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: The series expansions and Gauss-Legendre rule for computing arbitrary derivatives of the beta-type functions