Computing the Kummer function \(U\)(\textit{a, b, z}) for small values of the arguments

DOI10.1016/j.amc.2015.09.047zbMath1410.33008arXiv1509.05167OpenAlexW2176398240MaRDI QIDQ1732217

Amparo Gil, Nico M. Temme, Javier Segura

Publication date: 22 March 2019

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.05167

zbMATH Keywords

asymptotic approximationpower seriesnumerical computationKummer function

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Computation of special functions and constants, construction of tables (65D20) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15)

Related Items

Computation of the confluent hypergeometric function \(U(a,b,x)\) and its derivative for positive arguments, High-precision computation of the confluent hypergeometric functions via Franklin-Friedman expansion

Uses Software

• CONHYP
• DLMF

Cites Work

• Unnamed Item
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• The numerical computation of the confluent hypergeometric function U(a,b,z)
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• The Exponentially Convergent Trapezoidal Rule
• Algorithm 707: CONHYP: a numerical evaluator of the confluent hypergeometric function for complex arguments of large magnitudes
• Numerical evaluation of the Gauss hypergeometric function by power summations
• Numerical Methods for Special Functions
• Concerning Two Series for the Gamma Function
• Computing the confluent hypergeometric function, \(M(a,b,x)\)