Geodesic
Evaluation of many-electron atomic integrals using a Hylleraas-type basis
Numerical methods and programming, Tome 7 (2006) no. 1, pp. 50-60.

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A new version of the standard series expansion algorithm for calculation of one-center many-particle correlation integrals is proposed. The performance of this algorithm is considerably increased due to a special order of computation of auxiliary $W$-integrals using recurrent formulas to express one integral in terms of another integral. This technique allows one to compute an array of $W$-functions and to retain the numerical accuracy of computations by evaluating a small number of its components with the use of infinite series. Evaluation of $W$-integrals by infinite series and extrapolation procedures are also improved.
Keywords: many-particle integrals, Hylleraas-type basis, convergence acceleration. 
@article{VMP_2006_7_1_a6,
     author = {S. Ya. Ishchenko},
     title = {Evaluation of many-electron atomic integrals using a {Hylleraas-type} basis},
     journal = {Numerical methods and programming},
     pages = {50--60},
     publisher = {mathdoc},
     volume = {7},
     number = {1},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2006_7_1_a6/}
}
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S. Ya. Ishchenko. Evaluation of many-electron atomic integrals using a Hylleraas-type basis. Numerical methods and programming, Tome 7 (2006) no. 1, pp. 50-60. http://geodesic.mathdoc.fr/item/VMP_2006_7_1_a6/