Deducing the Properties of Singularities of Functions from their Taylor Series Coefficients

DOI10.1137/0139022zbMath0457.65003OpenAlexW2059280515MaRDI QIDQ3906975

No author found.

Publication date: 1980

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0139022

zbMATH Keywords

algorithmsnumerical examplesasymptotic behaviourconvergence propertiesTaylor series expansionsingularities of functionsDarboux's theoremNeville extrapolation

Mathematics Subject Classification ID

Singular functions, Cantor functions, functions with other special properties (26A30) Convergence and divergence of series and sequences (40A05) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Power series (including lacunary series) in one complex variable (30B10) Extrapolation to the limit, deferred corrections (65B05) Computation of special functions and constants, construction of tables (65D20) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58) Numerical summation of series (65B10)

Related Items

Resurgence and \( 1/N \) expansion in integrable field theories, A Borel transform method for locating singularities of Taylor and Fourier series, Reconstruction of spectra and an algorithm based on the theorems of Darboux and Puiseux, Quantum Fisher Information and Lee‐Yang Zeros with Quantum Coherence of the Isotropic XY$XY$ Model and the Energy Scale, Methods for the computation of the multivalued Painlevé transcendents on their Riemann surfaces, Two-dimensional bifurcation phenomena in thermal convection in horizontal, concentric annuli containing saturated porous media, Application of Hermite-Padé approximation for detecting singularities of some boundary value problems, Detecting and locating a singular point in the numerical solution of IVPs for ODEs, Hydrodynamic dispersion relations at finite coupling, Convergence analysis and detection of singularities within a boundary meshless method based on Taylor series, Large-degree asymptotics and exponential asymptotics for Fourier, Chebyshev and Hermite coefficients and Fourier transforms, The Eigenvalues of Mathieu's Equation and their Branch Points, On computing Darboux type series analyses, High order analysis of the limit cycle of the van der Pol oscillator, High-order differential approximants