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Fast and accurate method for summation of divergent series
Author(s) -
Fernández Francisco M.
Publication year - 2001
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/1097-461x(2001)81:4<268::aid-qua4>3.0.co;2-w
Subject(s) - divergent series , anharmonicity , series (stratigraphy) , power series , radius of convergence , convergence (economics) , algebraic number , padé approximant , zeeman effect , radius , rotor (electric) , physics , mathematics , mathematical analysis , summation by parts , quantum mechanics , computer science , magnetic field , paleontology , computer security , economics , biology , economic growth
We develop a particular case of algebraic approximants for the summation of divergent power series and for the continuation of such expansions beyond their radius of convergence. The calculation of bound states and resonances for one‐ and two‐dimensional anharmonic oscillators, for a perturbed rigid rotor, and for the Zeeman and Stark effects in hydrogen shows that the present method is one of the most efficient ones for that purpose. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 268–279, 2001