New properties of a certain method of summation of generalized hypergeometric series

DOI10.1007/s11075-016-0261-1zbMath1382.65008arXiv1602.08895OpenAlexW2963769872MaRDI QIDQ1678584

Paweł Woźny, Rafał Nowak

Publication date: 17 November 2017

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

Full work available at URL: https://arxiv.org/abs/1602.08895

zbMATH Keywords

numerical exampleconvergence accelerationsummation of generalized hypergeometric series

Mathematics Subject Classification ID

Extrapolation to the limit, deferred corrections (65B05) Computation of special functions and constants, construction of tables (65D20) Generalized hypergeometric series, ({}_pF_q) (33C20) Numerical summation of series (65B10) Numerical approximation and evaluation of special functions (33F05)

Uses Software

• DLMF

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Efficient algorithm for summation of some slowly convergent series
• Acceleration of generalized hypergeometric functions through precise remainder asymptotics
• Asymptotical formulas for Gaussian and generalized hypergeometric functions
• Interpolation between sequence transformations
• Method of summation of some slowly convergent series
• Sequence transformations and their applications
• A new method for deriving Padé approximants for some hypergeometric functions
• Extrapolation methods theory and practice
• A hierarchically consistent, iterative sequence transformation
• Scalar Levin-type sequence transformations
• Transformation formulas for the generalized hypergeometric function with integral parameter differences
• Convergence acceleration of orthogonal series
• Special values of the hypergeometric series II
• Certain transformations and summations for generalized hypergeometric series with integral parameter differences
• Extension of some classical summation theorems for the generalized hypergeometric series with integral parameter differences
• Acceleration of Linear and Logarithmic Convergence
• Practical Extrapolation Methods
• New summation technique for rapidly divergent perturbation series. Hydrogen atom in magnetic field
• An Analytic Method for Convergence Acceleration of Certain Hypergeometric Series
• On two Thomae-type transformations for hypergeometric series with integral parameter differences
• Development of non-linear transformations for improving convergence of sequences
• A note on T-transformation of Lubkin
• On a Device for Computing the e m (S n ) Transformation
• Convergence acceleration during the 20th century

This page was built for publication: New properties of a certain method of summation of generalized hypergeometric series