Study of a generalized Levin–Weniger convergence accelerator of numerical series: Particular cases and applications to multi-electron integrals in atomic physics

1972 Bender, 1978 Beshenov Bornemann, 2004 Brezinski, 1996, A derivation of extrapolation algorithms based on error estimates, J. Comput. Appl. Math., 66, 5, 10.1016/0377-0427(95)00157-3 Brezinski, 1991 Brezinski, 1994, A general extrapolation procedure revisited, Adv. Comput. Math., 2, 461, 10.1007/BF02521609 Brezinski, 1994, On the kernel of sequence transformations, Appl. Numer. Math., 16, 239, 10.1016/0168-9274(94)00054-9 Clark, 1969, A note on the T-transformation of Lubkin, J. Res. Natl. Bur. Stand. B, 73, 25, 10.6028/jres.073B.003 Čížek, 2003, New summation technique for rapidly divergent perturbation series. Hydrogen atom in magnetic field, J. Math. Phys., 44, 962, 10.1063/1.1541119 Delahaye, 1982, The set of logarithmically convergent series cannot be accelerated, SIAM J. Numer. Anal., 19, 840, 10.1137/0719059 Fousse, 2004, MPFR: A multiple-precision binary floating-point library with correct rounding, ACM Trans. Math. Software, 33, 13:1 Gil, 2007 Grotendorst, 1986, Efficient evaluation of infinite-series representations for overlap, two-center nuclear attraction, and Coulomb integrals using nonlinear convergence accelerators, Phys. Rev. A, 33, 3706, 10.1103/PhysRevA.33.3706 Jentschura, 1999, Convergence acceleration via combined nonlinear-condensation transformations, Comput. Phys. Comm., 116, 28, 10.1016/S0010-4655(98)00111-8 King, 1991, Analysis of some integrals arising in the atomic three-electron problem, Phys. Rev. A, 44, 7108, 10.1103/PhysRevA.44.7108 King, 1997, Progress on high precision calculations for the ground state of atomic lithium, J. of Mol. Struct. (THEOCHEM), 400, 7, 10.1016/S0166-1280(96)04919-6 Levin, 1973, Development of non-linear transformations for improving convergence of sequences, Int. J. Comput. Math. B, 3, 371, 10.1080/00207167308803075 Porras, 1994, Evaluation of some integrals for the atomic three-electron problem using convergence accelerators, Phys. Rev. A, 49, 1637, 10.1103/PhysRevA.49.1637 Press, 2007 Sack, 1964, Generalization of Laplace's expansion to arbitrary powers and functions of the distance between two points, J. Math. Phys., 5, 245, 10.1063/1.1704114 Sidi, 2003 Weniger, 1989, Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series, Comput. Phys. Rep., 10, 189, 10.1016/0167-7977(89)90011-7 Weniger, 2004, Mathematical properties of a new Levin-type sequence transformation introduced by Čížek, Zamastil, and Skála. I. Algebraic theory, J. Math. Phys., 45, 1209, 10.1063/1.1643787 Weniger, 2009, The strange history of B functions or how theoretical chemists and mathematicians do (not) interact, Int. J. Quantum Chem., 109, 1706, 10.1002/qua.22014 Weniger, 1989, Nonlinear sequence transformations for the efficient evaluation of auxiliary functions for GTO molecular integrals, 341