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Recursion relations for the three‐electron subsidiary integral W ( l , m , n ; α, β, γ)
Author(s) -
Li Chun,
Wang Liming,
Yan ZongChao
Publication year - 2012
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/qua.24284
Subject(s) - recursion (computer science) , logarithm , convergence (economics) , mathematics , series (stratigraphy) , electron , improper integral , mathematical analysis , integral equation , physics , mathematical physics , pure mathematics , quantum mechanics , singular integral , algorithm , paleontology , economics , biology , economic growth
The subsidiary integral W ( l , m , n ; α, β, γ) is a key integral that appears in the variational calculation of a three‐electron atomic system using Hylleraas coordinates. For the case where the ratio α/(α + β + γ) ∼ 1, an important special situation that may occur in the evaluation of the Bethe logarithm, existing approaches for calculating the W integral become impractical due to the problem of slow convergence. In this article, we present a computationally efficient and numerical stable method, in which the W integral can be expressed in terms of either a finite series or a finite recursion relation. Numerical tests are given. © 2012 Wiley Periodicals, Inc.