Numerically satisfactory solutions of Kummer recurrence relations

DOI10.1007/s00211-008-0175-5zbMath1154.65013OpenAlexW2128982402MaRDI QIDQ957938

Nico M. Temme, Javier Segura

Publication date: 1 December 2008

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://ir.cwi.nl/pub/12803

zbMATH Keywords

three-term recurrence relations\(_1F_1(abKummer hypergeometric functionz)\)

Mathematics Subject Classification ID

Computation of special functions and constants, construction of tables (65D20) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15) Numerical approximation and evaluation of special functions (33F05)

Related Items

On bounds for solutions of monotonic first-order difference-differential systems ⋮ Computation of the confluent hypergeometric function \(U(a,b,x)\) and its derivative for positive arguments ⋮ Computing the Kummer function \(U\)(\textit{a, b, z}) for small values of the arguments ⋮ Numerical methods for the computation of the confluent and Gauss hypergeometric functions ⋮ On the computation and inversion of the cumulative noncentral beta distribution function ⋮ Fast, reliable and unrestricted iterative computation of Gauss-Hermite and Gauss-Laguerre quadratures

Cites Work

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• Identifying minimal and dominant solutions for Kummer recursions
• Transitory minimal solutions of hypergeometric recursions and pseudoconvergence of associated continued fractions
• Numerically satisfactory solutions of hypergeometric recursions
• Uniform Asymptotic Expansions for Whittaker’s Confluent Hypergeometric Functions
• Numerical Methods for Special Functions