The numerical computation of the confluent hypergeometric function U(a,b,z)

DOI10.1007/BF01396306zbMath0489.33001MaRDI QIDQ1166687

Nico M. Temme

Publication date: 1983

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

Full work available at URL: https://eudml.org/doc/132840

zbMATH Keywords

asymptotic expansionsrecurrence relationsconfluent hypergeometric functionALGOL 60 programs

Mathematics Subject Classification ID

Computation of special functions and constants, construction of tables (65D20) Classical hypergeometric functions, ({}_2F_1) (33C05) Software, source code, etc. for problems pertaining to special functions (33-04)

Related Items (14)

Asymptotics and closed form of a generalized incomplete gamma function ⋮ Computation of the confluent hypergeometric function \(U(a,b,x)\) and its derivative for positive arguments ⋮ The Temme's sum rule for confluent hypergeometric functions revisited. ⋮ 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 ⋮ Incomplete Bessel, generalized incomplete gamma, or leaky aquifer functions ⋮ Orthogonal confluent hypergeometric lattice polynomials ⋮ Computation of a numerically satisfactory pair of solutions of the differential equation for conical functions of non-negative integer orders ⋮ Hyperdeterminants. I ⋮ Computing Hypergeometric Functions Rigorously ⋮ Numerical computation of Tricomi's psi function by the trapezoidal rule ⋮ The effect of barotropic instability on the nonlinear evolution of a Rossby-wave critical layer ⋮ Transitory minimal solutions of hypergeometric recursions and pseudoconvergence of associated continued fractions ⋮ Extended incomplete gamma functions with applications

Cites Work

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• On the expansion of confluent hypergeometric functions in terms of Bessel functions
• On the computation of Tricomi's \(\psi\) function
• On the numerical evaluation of the modified Bessel function of the third kind
• Numerical evaluation of functions arising from transformations of formal series
• On Temme's Algorithm for the Modified Bessel Function of the Third Kind
• Evaluation of Repeated Integrals of the Coerror Function
• Computational Aspects of Three-Term Recurrence Relations
• Numerical solution of second-order linear difference equations

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