Abstract
Some of the mathematical difficulties that arise in the evaluation of the Breit–Pauli relativistic energy corrections for the S states of three-electron systems are resolved. Evaluation of the expectation value of the Breit–Pauli Hamiltonian using explicitly correlated wave functions leads to sets of integrals that diverge individually. By appropriately combining these integrals, and using some judicious series expansions, all the integration problems are resolved in terms of well-known auxiliary functions.
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