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- W2065273216 abstract "The convergence of large-order expansions in δ=1/D, where D is the dimensionality of coordinate space, for energies E(δ) of Coulomb systems is strongly affected by singularities at δ=1 and δ=0. Padé–Borel approximants with modifications that completely remove the singularities at δ=1 and remove the dominant singularity at δ=0 are demonstrated. A renormalization of the interelectron repulsion is found to move the dominant singularity of the Borel function F(δ)=∑jEj′/j!, where Ej′ are the the expansion coefficients of the energy with singularity structure removed at δ=1, farther from the origin and thereby accelerate summation convergence. The ground-state energies of He and H2+ are used as test cases. The new methods give significant improvement over previous summation methods. Shifted Borel summation using Fm(δ)=∑jEj′/Γ(j+1−m) is considered. The standard deviation of results calculated with different values of the shift parameter m is proposed as a measure of summation accuracy." @default.
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- W2065273216 date "1998-10-01" @default.
- W2065273216 modified "2023-09-27" @default.
- W2065273216 title "Improving the convergence and estimating the accuracy of summation approximants of 1/D expansions for Coulombic systems" @default.
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- W2065273216 doi "https://doi.org/10.1063/1.532561" @default.
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