Use of nonlinear convergence accelerators for the efficient evaluation of GTO molecular integrals

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Abstract
Different methods for accelerating convergence of known series expansions for the auxiliary functions Fm(t) encountered in molecular integrals over Gaussian-type orbitals have been tested and compared. We have investigated the numerical properties of the Shanks transformation and the Levin transformations. It turns out that Levin’s t transformation is the best accelerator, whereas the Shanks transformation, which nearly yields the same results as the continued-fraction method, is less effective.

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