Shanks' convergence acceleration transform, Padé approximants and partitions

DOI10.1016/0097-3165(86)90024-5zbMath0617.41030OpenAlexW2092511106MaRDI QIDQ1821982

George E. Andrews, David M. Jackson, Ian P. Goulden

Publication date: 1986

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0097-3165(86)90024-5

zbMATH Keywords

Padé approximantslittle q-Jacobi polynomials

Mathematics Subject Classification ID

Approximation by rational functions (41A20)

Related Items (max. 100)

Extrapolation from hypergeometric functions, continued functions and Borel-Leroy transformation; resummation of perturbative renormalization functions from field theories ⋮ The genesis and early developments of Aitken's process, Shanks' transformation, the \(\varepsilon\)-algorithm, and related fixed point methods ⋮ Continued functions and perturbation series: simple tools for convergence of diverging series in \(\mathrm{O}(n)\)-symmetric \(\phi^4\) field theory at weak coupling limit ⋮ Padé approximants for the q-elementary functions ⋮ Twin Nicomachean q-identities and conjectures for the associated discriminants, polynomials, and inequalities ⋮ Continued functions and Borel–Leroy transformation: resummation of six-loop ϵ-expansions from different universality classes

Cites Work

• Two theorems of Gauss
• Two theorems of Gauss and allied identities proved arithmetically
• Orthogonal Polynomials and Hypergeometric Series
• A GENERAL SYSTEM OF ORTHOGONAL POLYNOMIALS
• Über Orthogonalpolynome, die q‐Differenzengleichungen genügen
• On the Transformation Theory of Basic Hypergeometric Functions
• A Short Proof of an Identity of Euler
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