Geodesic
Computing the sums of Rayleigh–Schrödinger series of perturbed self-adjoint operators
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 9, pp. 1494-1505

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A new method is proposed and validated for computing the sums of number series of discrete operators in perturbation theory with the required accuracy. Its efficiency is demonstrated through numerical computations. 
@article{ZVMMF_2007_47_9_a4,
     author = {S. I. Kadchenko},
     title = {Computing the sums of {Rayleigh{\textendash}Schr\"odinger} series of perturbed self-adjoint operators},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1494--1505},
     publisher = {mathdoc},
     volume = {47},
     number = {9},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_9_a4/}
}
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S. I. Kadchenko. Computing the sums of Rayleigh–Schrödinger series of perturbed self-adjoint operators. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 9, pp. 1494-1505. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_9_a4/