Acceleration of sequences with transformations involving hypergeometric functions

DOI10.1007/s11075-022-01334-7zbMath1506.65005OpenAlexW4281909825MaRDI QIDQ2679691

Rafael Tristão Pepino

Publication date: 23 January 2023

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

Full work available at URL: https://doi.org/10.1007/s11075-022-01334-7

zbMATH Keywords

divergent seriessummation of seriesacceleration of convergenceiterative sequence transformationlinearly convergent sequencelogarithmically convergent sequence

Mathematics Subject Classification ID

Numerical summation of series (65B10) Acceleration of convergence in numerical analysis (65B99)

Uses Software

• DLMF

Cites Work

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• The genesis and early developments of Aitken's process, Shanks' transformation, the \(\varepsilon\)-algorithm, and related fixed point methods
• Construction of new generalizations of Wynn's epsilon and rho algorithm by solving finite difference equations in the transformation order
• The Set of Logarithmically Convergent Sequences Cannot be Accelerated
• The summation of the ordinary and renormalized perturbation series for the ground state energy of the quartic, sextic, and octic anharmonic oscillators using nonlinear sequence transformations
• A Convergence Acceleration Method for Some Logarithmically Convergent Sequences
• Practical Extrapolation Methods
• Development of non-linear transformations for improving convergence of sequences
• The Mathematica GuideBook for Symbolics
• Divergence of Perturbation Theory in Quantum Electrodynamics
• On a Device for Computing the e m (S n ) Transformation
• Convergence acceleration during the 20th century

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