A recursive algorithm for an efficient and accurate computation of incomplete Bessel functions

DOI10.1007/s11075-022-01438-0zbMath1506.65004arXiv2204.11197OpenAlexW4308264592MaRDI QIDQ2679694

Richard Mikael Slevinsky, Hassan Safouhi

Publication date: 23 January 2023

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2204.11197

zbMATH Keywords

numerical integrationextrapolation methodsincomplete Bessel functionsSlevinsky-Safouhi formulae\(G\) transformation

Mathematics Subject Classification ID

Extrapolation to the limit, deferred corrections (65B05) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Numerical integration (65D30)

Uses Software

• DistributionUtils

Cites Work

• Useful properties of the coefficients of the Slevinsky-Safouhi formula for differentiation
• A recursive algorithm for the \(G\) transformation and accurate computation of incomplete Bessel functions
• Fast ewald summation based on NFFT with mixed periodicity
• New formulae for higher order derivatives and applications
• Two new classes of nonlinear transformations for accelerating the convergence of infinite integrals and series
• Incomplete Bessel, generalized incomplete gamma, or leaky aquifer functions
• Computation of Tail Probabilities via Extrapolation Methods and Connection with Rational and Padé Approximants
• INCOMPLETE BESSEL FUNCTIONS. I
• A New Method for Approximating Improper Integrals
• INCOMPLETE BESSEL FUNCTIONS. II. ASYMPTOTIC EXPANSIONS FOR LARGE ARGUMENT
• Nonlinear Transformations Related to the Evaluation of Improper Integrals. I
• Theory of Incomplete Cylindrical Functions and their Applications
• Survey of Extrapolation Processes in Numerical Analysis
• Higher OrderG-Transformation

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